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ON THE NATURE
OF LIGHT
PROF. G. G. STOKES
i
iniiiiiiii
p
600048708X
I'SSX £. 75
BURNETT LECTURES.
ON LIGHT.
\
BURNETT LECTURES.
ON LIGHT.
PRINTED BY C. J. CLAY, M.A. & SON,
AT THE UNIVERSITY PRESS*
PREFACE.
The lectures, of which the first course is con-
tained in the present volume, originated in a
new direction given to an old endowment. Mr
John Burnett, merchant in Aberdeen, who died
in 1784, bequeathed the greater part of his
property to various charitable and pious objects.
Among others, a portion of the property was
vested in trustees for establishing prizes for the
best and next best essay on the following sub-
ject : —
"That there is a Being, all-powerful, wise, and
good, by whom everything exists; and particularly
to obviate difficulties regarding the wisdom and gpod-
ness of the Deity ; and this, in the first place, from
considerations independent of written revelation,
s. b
VI PREFACE.
and in the second place, from the revelation of the
Lord Jesus; and, from the whole, to point out the
inferences most necessary for, and useful to man-
kind."
These essays were to be competed for at
intervals of 40 years, and awards have been
made on two occasions since the original foun-
dation.
But it was thought that the production of
essays at such long intervals did not form a
satisfactory mode of utilizing the bequest of the
founder ; and in 1881 a new direction was given
to the foundation by an order of the Secretary
of State for the Home Department, in accord-
ance with the provisions of the Endowed Insti-
tutions (Scotland) Act of 1878. By this order
it was provided that a Lecturer should be
appointed at intervals of 5 years, to hold office
for 3 years, the subject of the lectures being
determined by the following regulation : —
" The Trustees and assessors may prescribe as the
subject of the course of lectures that specified in the
PREFACE. VU
codicil to the will of the testator, viz. [as above]. Or
otherwise, the trustees may prescribe, as the subject
of any course of lectures, recent researches (as at the
date of the appointment) into any of the following
branches of knowledge, viz : —
1. History, including the illustrations of the forms
and effects of theistic doctrines among the older
nations of the world.
2. Archaeology.
3. Physical science.
4. Natural science.
And they shall instruct the lecturer to have regard,
in treating of the special subject prescribed, to the
illustration afforded by it of the theme proposed by
the testator, and that under such conditions or qualifi-
cations as they may prescribe."
The Trustees selected physical science as the
subject of the first lectures under the new system,
and they did me the honour of appointing me
the first Burnett Lecturer. It has been arranged
that four lectures are to be given each year of
office, and that the subject of the complete course
shall be Light, the subject being treated under
three divisions, to which the lectures in each
year are to be respectively devoted. The first
. •••
vm PREFACE.
division IS sufficiently explained by the title of
the present course ; the subjects of the second
and third divisions will be found at the end of
the fourth lecture.
I am sensible of the difficulty of the task I
have attempted in this first year's course,
namely, while avoiding all mathematical details,
to give the audience some fair idea of the evi-
dence on which we accept the views respecting
the nature of light which are at present held, I
may almost say universally, in the scientific
world. I assume on the part of the reader a
knowledge of the rectilinear propagation of light
in the same medium, of the laws of reflection and
refraction, of the compound character and of the
decomposition of white light ; but I have not
assumed that he is acquainted with the phe-
nomena of interference, or diffraction, or double
refraction, or polarization, though some acquain-
tance with these subjects will make the lectures
much more easy to follow. For the sake of
those persons to whom these things may be
PREFACE. IX
nearly or entirely new, I have been obliged to
enter into details which I cannot help fearing
may be wearisome to those who have already a
pretty good acquaintance with the subject ;
though I hope that even they may not find the
weighing of the evidence wholly uninteresting
or unprofitable.
G. G. STOKES.
Cambridge,
February 5, 1884.
CONTENTS.
LECTURE I.
PAGE
Bearing of the more obvious properties of Light on our view of its
nature — ^Theories of emission and of undulations — Colours of
thin plates — Newton's attempt to explain them on the theory
of emission — Insufficiency of the explanation . . . • i
LECTURE II.
Interference — Explanation of the colours of thin plates afforded by
the theory of undulations — ^Diffiraction 31
LECTURE III.
Closer examination of the fundamental suppositions of the Theory
of Undulations— Survey of the conclusions arrived at by a
study of the phenomena of common light — Elementary facts of
double refraction and polarization 74
LECTURE IV.
Phenomena presented on interposing a crystalline block or thin
plate in the path of Polarized Light which is subsequently
analyzed — Laws on Interference of Polarized Light — ^Theory
of Transverse Vibrations — Conclusion 105
■^
LECTURES ON LIGHT.
FIRST COURSE.
On the Nature of Light.
LECTURE I.
Bearing of the more obvious properties of Light on our view
of its nature — Theories of emission and of undulations —
Colours of thin plates — Newton's attempt to explain them
on the theory of emission — Insuffiiien<y of the explanation.
Among all our senses, there is none more wonder-
ful than that of sight. It confers upon us, as Sir
John Herschel has remarked, to a considerable extent
the character of ubiquity. It is accordingly a matter
of extreme interest to iind out what we can as to the
mode in which this end so important to our well-
being is brought about ; whether it be by investigat-
ing the properties of any agent external to ourselves
which may be concerned in its accomplishment, or
by seeking to penetrate some little way into that
2 THE NATURE OF LIGHT.
mysterious chain of sequence which connects the
external agent with the sensation conveyed to our
minds. It is true indeed that there is no prospect of
our being able to bridge over the gulf which sepa-
rates mind from matter; yet there are many things
to indicate that that mysterious organ which we pos-
sess, the brain, has some intimate connexion with
the operations of the mind, and we can do something
towards tracing a connexion between the part of our
bodies directly affected by the external agent and the
brain ; a connexion of such a kind as to leave no
doubt that it forms the means whereby the immediate
action of the external agent is ultimately perceived
by the mind ; though how the final conveyance takes
place is a mystery we are not likely to fathom.
But this does not prevent us from being able to
trace some links in the chain of connexion, nor from
recognizing the evidences of design which that portion
which we can in a measure follow is calculated to
impress upon us.
I have spoken of an external agent even though
it was more especially the sense of sight that I had
in view. We are so accustomed to the contemplation
of an objective somethings which we call Light, as the
external agent by the action of which vision is in
some way brought about, that we have a difficulty fn
conceiving how anyone could think otherwise. We
IDEAS OF THE ANCIENTS. 3
see the objects in a room, but it is matter of the
commonest observation that though the objects may
be there and our eyes may be there, we see them not
if it be night, or if the room be closely shut up, until
a lighted lamp or candle or something of the kind is
introduced. We recognize the flame as the seat of
some influence, to which we give the name of light,
which is essential to vision. Yet obvious as this
proposition appears to us, it is remarkable that it was
not always so. At least one writer of acute intellect
in ancient times held that it was something emanating
from the eye, not something from without entering
into it, that enabled us to perceive distant objects.
This shows by what a slow and gradual progress
our knowledge of physical science is built up. We
are accustomed to vaunt of our knowledge in this
19th century; yet it may be that generations hence
the scientific men of the day will wonder how we
could have failed to perceive things which to them
will appear quite obvious.
A self-luminous body then is, as such, a source of
an influence which can be exerted at a distance. In
this respect it by no means stands alone ; two bodies
at a distance from one another may for example
influence each other through the attraction of gravi-
tation, and other modes of influence might also be
mentioned, but I will confine myself to gravitation*
1—2
4 THE NATURE OF LIGHT.
Now between these two modes of influence there are
great and striking differences. One of the most
salient is this, that in the case of gravitation the
influence is exerted independently of the interposition
of matter of any kind^ whereas in the case of light
the influence is capable of being arrested by an
extremely thin screen of matter of a suitable kind ;
for example, silver foil, or a film of Indian ink spread
on glass.
The consideration of a screen leads us naturally
to another fundamental and very obvious property of
light. Suppose the screen pierced by one or more
rather small apertures ; how will the influence beyond
the screen be distributed? We find that it is per-
ceived only within the projections of the aperture or
apertures made by straight lines drawn from the
luminous body, which for simplicity I here suppose to
be a point
This indeed is not rigorously true, for about the
boundary of the projection of the aperture, that is,
near the projection of the edge of the aperture, there
is a gradual, not sudden, passage from light within
to darkness outside, accompanied by fluctuations of
greater and less luminosity which I cannot now enter
into particularly ; and when the aperture is extremely
small, the spreading out of the light which passes
through it is by no means very small compared with
RECTILINEAR PROPAGATION, 5
the breadth of the projection of the aperture itself.
Nevertheless in ordinary cases the spreading out of
the light is so small that we may disregard it, and
say that light proceeds from a luminous point in all
directions in straight lines until it is stopped by some
obstacle. It will be understood that I am here speak-
ing of light only as it passes in free space, or which
comes to nearly the same thing, in air, and not from
one medium into another.
When I speak of light proceeding /n7/« a luminous
point, all I wish to express is that we recognize the
luminous point as the seat or origin of a certain
influence which is exerted, though with an intensity
which diminishes with increasing distance, at all
points from which a straight line can be drawn with-
out interruption to the luminous point ; I do not wish
to imply the idea of motion, or propagation of any
kind* The feature therefore that we are at present
considering is common to light and gravitation.
A very important question now arises, Do these
influences take time to travel, or does the influence
exerted at any moment of time depend solely on the
state and position of the two bodies, the influencing
and the influenced, at that moment ? The idea which
we may be led to form as to the nature of light must
depend most materially on the answer we have to
give to this question as applied to light
6 . THE NATURE OF LIGHT.
That light is propagated in time, cannot be inferred
from ordinary observation. Thus when a landscape
is illuminated at night by a flash of lightning or an
eixplosion of gunpowder, the flash and the objects
illuminated by it are seen, so far as our senses can
decide, simultaneously, though in the latter case the
light has to travel from the flash to the object
illuminated, and from that to the eye, instead of
coming straight from the flash. As far as ordinaty
observation goes, then, the question whether any time
is occupied in the transmission is left an open one,
and we can only say that if time is required for
transmission, the rate of travelling must be enormously
great.
But in the solar system we have distances to deal
with Compared with which the dimensions of the
earth itself on which we dwell, let alone those of a
landscape, sink into insignificance. It is conceivable
that in. travelling over those vast distances, if it does
travel at all, light might occupy lengths of time
which would not be insensibly small, and which"
possibly might be put in evidence by some celestial
phenomenon. Thus if the light of the sun were
emitted by flashes, the sun would take the place of
the thnnder-cloud in our supposed observation, and
the iplariets that of the objects' in the landscape.
Though there are fchanges going on in the sun, as we
VELOCITY OF PROPAGATION. 7
now know, there are none of such magnitude and
suddenness as to be available for such an observation^
Nevertheless it was by celestial observations, of a
somewhat different kind, that the finite velocity of
light was first revealed.
This was done as long ago as in 1676 by Roemer,
who showed that an inequality in the times of
occurrence of the eclipses of Jupiter's satellites, which
he had observed, was simply^ explicable on the
supposition that light is propfligated with a finite
velocity. The mean motion of a satellite round the
planet being accurately known, from observations
extending over a sufficient time, the times of suc-
cessive eclipses can be calculated. It was found that
the eclipses happened earlier or later than the calcu-
lated times, supposing the epoch so chosen as to make
the accelerations and retardations balajlce on an
average, according as the earth and Jupiter were on
the same side of the sun or on different sides, and
the differences in the apparent errors in the times of
occurrence of the eclipses at different times of the
year were proportional to the differences of the dis*
tances of Jupiter from the earth at those times.
The greatest difference in that distance is evidently
equal to the diameter of the earth's orbit (supposing
for simplicity the orbits of the earth and Jupiter cir-
cular and in the same plane), and to this corresponds
8 THE NATURE OF LIGHT.
the greatest difference in the apparent errors of the
times of occurrence, which amounts to about i6
minutes and a quarter. We learn therefore that if
this be the true reason of the observed inequality,
light takes 8 minutes and a few seconds to travel
over the distance from the earth to the sun. To ex-
press the velocity in miles per second, we require to
know the dimensions of the earth's orbit, or what
comes to the same the solar parallax, which, being
the ratio of the radii of the earth and the earth's
orbit, serves to express the latter in miles since the
former is accurately known. According to the value
of the sun's parallax which was accepted till recent
years, the velocity of light so determined came out
about 192,000 miles per second. More recent de-
terminations have reduced this to about 186,000 miles
per second.
For nearly 50 years after Roemer's discovery, no
other phenomenon was known which indicated that
the propagation of light was other than instan-
taneous ; but then Bradley made the very remarkable
discovery of the aberration of light. It would
occupy too much time to go fully into this, and I
must content myself with giving you a general notion
of it.
Suppose a person out on a perfectly calm day
when rain was falling, and accordingly, on account of
ABERRATION OF LIGHT. 9
the perfect calmness supposed, falling vertically. If
the person were at rest, he would deem the rain to be
falling vertically. But suppose he were carried hori-
zontally along with a motion so smooth that he was
unconscious of it. The rain though falling vertically
would appear to him to fall in a somewhat slanting
direction, as if it came from a point not exactly
in the zenith, but displaced from it towards the
point towards which the observer is being carried.
And if instead of falling vertically the rain be
falling in a slanting direction, it will appear to the
observer, unconscious of his own motion, to slant
differently ; in fact, if we compound the velocity of
the falling rain with a velocity equal and opposite
to that of the observer, the direction of motion of
the rain will appear to be that of the resultant
velocity.
Now Bradley found that just the same thing takes
place with regard to light. The earth in revolving
round the sun moves at the rate of about 20 miles in
a second, towards a point in the heavens lying in the
plane of the ecliptic 90® in advance of the heliocentric
position of the earth, or rather what would be 90*
if the earth's orbit were strictly circular. The light
which comes from any particular star appears to come
from a place deviating from the true place of the star
towards the point of the heavens towards which the
lO THE NATURE OF LIGHT.
earth is moving. And as this point goes round the
ecliptic in the course of a year, the apparent place of
the star describes annually a closed curve, in fact, a
small ellipse, round the mean position of the star.
The law of the apparent displacement of the star is
found to be what it oiight to be on the supposition
that the cause of it is what has been above explained,
and the coefficient of the displacement gives the ratio
of the velocity of light to that of the earth in its
orbit We are thus furnished with a second means of
determining the velocity of light, and observation
will show whether tlie two do or do not agree. The
result is a remarkably close agreement when we
consider on the one hand the difficulty of fixing on
the exact moment of disappearance of a satellite
which enters the shadow of Jupiter, and on the other
the smallness of the displacement which constitutes
aberration, amounting at a maximum to only 20
seconds and a quarter of angle, about the angle
subtended by a six-inch rule at the distance of a
mile«
It is to be noted that the unit of length in terms
of which the velocity of light in both of these
methods is primarily expressed is the radius of the
earth's orbit, and in order to translate it into miles
per second we require to know the solar parallax.
While I am on this point I may mention that in
EXPERIMENTAL DETERMINATION OF VELOCITY. TI
the year 1849 Fizeau, by an extremely ingenious
combination of apparatus, succeeded in determining
for the first time the velocity of light by direct
experiment. The resulting value was confirmatory"
of the two astronomical determinations, but was not
at first considered as capable of being put in com-
petition with them for accuracy, and no wonder, since
the whole interval of time to be measured in Fizeau's
experiment, under the circumstances in which it was
performed, amounted to only about the one tweilty'
thousandth "part of a second. Subsequent determi-
nations, however, first by Foucault, by a» different
method, and afterwards by Cornu, by Michelson, and
by the late Dr James Young and Prof. G. Forbes,
by one or other of those methods modified, have
rendered the determination 450 certain and accurate
that it is probably quite equal in accuracy to the
astronomical determinations. And since the experi-
mental determination gives the velocity in terms of a
known distance on the earth's surface, and accordingly,
in miles or kilometres per second, if we assume the
experimental and either of the astronomical determi^
nations as separately valid and sufficiently, accurate,
by comparing the two we can determine the" radius of
the earth's orbit, which fixes the scale of the whole
solar system, in miles or "kilprnetr^s. A^d as we; knotv
accurately the dimensions of the earth, we can thus
12 THE NATURE OF LIGHT.
determine the solar parallax, by combining accurate
measurements of an astronomical phenomenon fre-
quently recurring or constantly going on with a
laboratory determination made once for all.
I have been tempted into a digression by the
interest of this subject, and I would now resume the
consideration of some of the elementary properties of
light, with a view of showing how we are gradually
led to the formation of a theory, now thoroughly
tested, as to the nature of Light itself.
The observations to which I have last alluded
show that light, whatever it may be, takes time to
travel, so that in speaking of light as an influence
that proceeds from a source of light there is no
longer occasion to exclude the idea of motion of some
sort* I have compared and contrasted two influences
of which I have spoken, light and gp-avitation, and in
this last point again it is a contrast with which we are
presented ; or at least if the two are analogous the
analogy has never yet been established. After having
ascertained that light takes time to travel, and con-
templated that exceedingly curious phenomenon re-
lating to light, aberration, the question naturally
presents itself to the mind, Is there anything analo-
gous as regards gravitation ? Does it like light take
time to travel, or is it an instantaneous influence?
Now the consequences which would follow as regards
THEORIES OF EMISSION AND OF UNDULATIONS. 1 3
the motions of the bodies of the solar system if
gravitation like light took time to travel have been
calculated, and it has been concluded that if the
influence of gravitation takes time to travel, it at any
rate travels incomparably more quickly than light,
with a velocity accordingly which is incomparably
greater than 186,000 miles per second.
I have reduced to a minimum the mention I have
made of the fundamental properties of light, in order
not to weary you by repeating what is to be found in
every text book, and we may now attack the question,
What notion are we to form of the intrinsic nature of
this agent, so important to our well-being, so won-
derful in the scale of magnitude of the quantities it
brings before us, as we have seen already as regards
the velocity with which it is propagated, and shall see
later on in other respects ?
There appear to be but two modes possible of
conceiving of a mechanical influence emanating from
an influencing body, travelling with a finite velocity,
and ultimately influencing another body at a distance,
A mechanical influence implies the action of matter
of some kind, and this matter we may suppose to
have been either darted forth, in the manner of a
projectile, or to have previously existed in the space
between the influencing and the influenced body, to
have been disturbed by the influencing body, and
14 THE NATURE OF LIGHT.
then to be successively agitated in successive portions,
each portion being agitated by its predecessor, and
in its turn yielding to its successor the disturbance
so received. We have not far to go to find illustrations
of both these kinds of action. Bullets exemplify the
first ; the progress of waves at the surface of water
illustrates the . second. A still better illustration,
except that it is not visible, is afforded by the
phenomena of sound.
Such accordingly are the ideas which lie at the
base of the two theories as to the nature of light which
for a long time divided the scientific world between
them, the corpuscular theory, or theory of emission,
and the theory of undulations.
Prima facie there is much to be said in favour of
the theory of emission. It lends itself at once to the
explanation of the rectilinear propagation of light,
and the existence of rays and shadows. It falls in at
once with the law of aberration. The laws of reflection
and refraction admit of an easy explanation in ac-
x:ordance with it ; at least if we except the existence
of both reflection and refraction ; for according to this
theory we should rather have expected beforehand
that light would have been either reflected or refracted,
according to circumstances, not that incident light
should have divided into a portion reflected and a
portion refracted.
THEORIES OF. EMISSION AND OF UNDULATIONS. 1 5
The theory of undulations on the other hand
presents at the outset considerable difficulties.' In
the first place it requires us to suppose that the
interplanetary and interstellar spaces are not, strictly
speaking, a vacuum but a plenum ; that though desti-
tute of ponderable matter they are filled with a sub-
stance of some kind, constituting what we call a
medium^ or vehicle of transmission of the supposed
undulations. When I speak of this medium as a
substance, or as material, I mean that it must possess
that distinctive property of matter, inertia ; that is to
say a finite time must be required to generate in a
finite portion of it a finite velocity. The necessity of
thus filling space with substance seems to have pre-
sented a serious difficulty to some minds. In the
course of a conversation with Sir David Brewster,
who had just returned from France, where he wit-
nessed the celebrated experiment by which Foucault
had just proved experimentally that light travels
faster in air than in water, I asked him what his
objection was to the theory of undulations, and I
found he was staggered by the idea in limine of
filling space with some substance merely in order
that "that little twinkling star," as he expressed
himself, should be able to send its light to us.
I cannot say that this particular difficulty is one
which ever presented itself as such to my own mind.
1 6 THE NATURE OF LIGHT.
To me the difficulty is rather that of conceiving such
an influence as that of gravitation to extend across
an absolute void. Such was the feeling of the great
discoverer himself of universal gravitation. In a
letter to Bentley, quoted by Faraday as falling in
with his own views, Newton thus expressed himself: —
"That gravity should be innate, inherent and
essential to matter, so that one body may act on
another at a distance through a vacuum^ without the
mediation of anything else, by and through which their
action and force may be conveyed from one to another,
is to me so great an absurdity, that I believe no man
who has in philosophical matters a competent faculty
of thinking, can ever fall into it. Gravity must be
caused by an agent acting constantly according to
certain laws ; but whether this agent be material or
immaterial, I have left to the consideration of my
readers."
If the supposition that light consists in undulations
obliges us to suppose that space is filled with some
kind of substance, at least as far as the remotest star
that our most powerful telescopes reveal to us, may
it not be that that same substance forms, in some
manner as yet unknown to us, the link of connexion
whereby the sun is enabled to attract the earth, and
keep it in its orbit ? It is true that notwithstanding
the labours of various scientific men we are not in a
LUMINIFEROUS ETHER, * I/.
condition to give an explanation of gravitation, T)ut
our inability to explain it by no means proves that it
is a primary property of matter, incapable of explana-
tion, or forbids us to suppose that it may in some way
be brought about through the intervention of that
same substance which we find necessary to assume
for the explanation of the phenomena of light on the
theory of undulations. And it is quite conceivable^
and we may now say even probable, that this same
substance has yet other offices to fill. Perhaps the
most remarkable of all the investigations of the late
Professor Clerk Maxwell is that in which he showed
that there is a certain velocit}'', numerically determine
able by purely electrical experiments which can be
made and have been made in the laboratory, and
expressing the velocity of propagation of an electrical
state, which is identical with the velocity of light
within the limits of error of the experiments and
observations whereby the two have been determined.
Assuming for the moment, as a thing at the present
day resting on evidence quite overwhelming, that
light consists of undulations, we cannot fail to be
impressed by the multiplicity of purposes, all bearing
so intimately on our well-being, which it seems pro^
bable, or not unlikely, are fulfilled by one and the
same substance, endowed with properties which we
are only gradually learning.
S. 2
1 8 THE NATURE OF LIGHT.*
1 have ventured to allude for a moment to the
present state of the theory of light, and I will now
go back. The necessity of assuming the existence of
some kind of substance in what we commonly speak
of as a vacuum, does not appear to have been a serious
preliminary difficulty in the way of the reception of
the theory of undulations. A far more formidable
difficulty appeared at first to be presented by the
existence of rays and shadows. It was this that led
Newton to adopt the theory of emission, though even
he was led in the course of his researches on light to
suppose that there was some sort of medium through
which the particles of light moved, and in which they
were capable in certain cases of exciting a sort of
undulation. But the supposition of particles darted
forth seemed to him necessary to account for shadows.
If light consisted simply of an undulation propagated
through a medium of some kind filling the interstellar
spaces, as we know sound consists of an undulatory
movement propagated in the air, how can we conceive
of the existence of shadows, knowing as we do that
sound passes freely round corners, and diverges after
passing through apertures, though indeed it is true
that the freedom is not absolute ? Newton's contem-
porary Huygens was more bold, and adopted the
theory of undulations pure and simple, rejecting
altogether the notion of particles darted forth from
DIFFICULTY OF EXPLANATION OP RAYS. 19
the' luminous body, and travelling with the Velocity
of light. Huygens made a grand attempt to explain
the existence of rays, the great stumbling-block at the
threshold of the theory of undulations. The principle
which goes by his name lies at the very foundation of
the theory of undulations, and itself rests on a strictly
mechanical basis, being in fact merely an application
to the particular question under consideration of the
general dynamical principle of the superposition of
small disturbances. But this principle does not by
itself alone suffice for the explanation of rays. It
proves, or at least appears to prove, too much. It
is as applicable to sound as, on the supposition that
light consists in undulations, it is to light; and if
Huygens's explanation of rays were complete there'
ought equally to be rays of sound, and sound ought
to present the same sharp shadows as light.
Huygens attempted to get over this difficulty by
entering on certain speculations as to the ultimate
constitution of the ether^ as we call the supposed
medium which is the vehicle of light, and as to the
mode of action, one on another, of the ultimate mole-
cules of which he imagined it to consist. In this he
abandoned the simplicity of the fundamental concep-
tions of the theory of undulations, and adopted a,
mode of reasoning not strictly allowable. For the
transmission of regular undulations, of which the.
2 — 2
20 THE NATURE OF LIGHT.
period IS arbitrary, at least within wide limits, requires
us to suppose that the transmitting medium is either
continuous or may be treated as such; that if it
consist of ultimate molecules, or be otherwise hetero-
geneous, the number of intervals from molecule to
molecule, or of deviations of one sign or another from
an average homogeneity, shall be very great and as
good as infinite within the length of a single undula-
tion ; and we have no right to extend to the medium
treated as a whole, and regarded as continuous, a
mode of communication of motion applicable only to
the communication from one to another of a set of
discrete molecules.
Accordingly, notwithstanding all that Huygens
has done, the existence of rays and shadows, one of
the most obvious properties of light, had received no
satisfactory explanation on the theory of undulations
such as it came from the hands of Huygens ; and in
this condition it remained for considerably more than
a century. His explanation of the laws of reflection
and refraction leaves nothing to be desired, except in
so far as these laws involve the conception of rays. I
cannot now speak of his discovery of the laws of
double refraction in Iceland spar, because it belongs
to a different branch altogether of the subject.
The theory of rays and shadows long remained in
this unsatisfactory state ; in fact, till quite the end of
PROGRESS OF THE TWO THEORIES. 21
the last century. Newton's discovery of the com-
pound nature of white light showed that there must
be in light an element of some kind susceptible of
continuous variation. Each theory, the corpuscular
and the undulatory, furnishes elements susceptible of
continuous variation. What the element is, on the
theory of emission, has not, so far as I know> been
specified by the supporters of that theory, and diffi-
culties seem to attend whatever supposition in that
respect you can make. The theory of undulations
presents one, and I may say but one, element which
might serve for the purpose, namely, wave length, or
what comes to the same thing, periodic time. That
in fact periodic time must be the element variations
in which correspond to variations in refrangibility, is
clearly pointed out by other phenomena which I have
not as yet touched upon. But this development of
the theory did not take place till the present century,
though some of the leading facts on which it is based
were known to and studied by Newton. Accordingly
from the time of Newton till the end of the last
century, and even further, the theory of emission was
that chiefly in vogue with scientific men. Various
causes probably contributed to this result. The
rectilinear propagation of light at first sight looks
more like the motion of projectiles than the propa-
gation of undulations, which in ca3es of what are
22 THE NATURE OF LIGHT.
undoubtedly undulations spread out much after being
laterally confined. The impetus given to the study
of the motion of particles under the action of known
forces by Newton's great discovery of univfcrsal gravi-
tation, turned the labours of men of science into that
channel rather than to a study of the propagatitm
of vibrations. The great weight again of Newton's
authority had doubtless its share in leading men to
follow the theory as to the nature of light which he
had taken up.
It is probably due to this preponderating influence
of the theory of emission that so little notice was
taken of the theory of the aberration of light. In the
explanation of the phenomenon which is contained in
the ordinary text-books of astronomy, which has
doubtless descended traditionally from that given in
earlier treatises, it is quietly assumed as a matter of
course that the rectilinear propagation of the light
coming from a heavenly body is not disturbed by the
motion of the earth. Did light consist of particles
darted forth, there is no reason to suppose that it
should ; in fact, to make such a supposition would
be to fly in the face of all we know respecting the
action of attracting forces, since any motion of the
attracting body does not enter into account. But on
the theory of undulations it is far otherwise. We
should naturally have been disposed to look on the
ABERRATION ON. THEORY OF UNDULATIONS. 23
earth in its motion round the sun as ploughing Its
way through the ether. Now if h'ght consist of un-
dulations propagated through this ether, we might
have expected that the ether being pushed by the
earth out of its way, the course of the undulations
which it carried would be affected, possibly in an
irregular way, in case eddies were produced, and at
any rate in a manner which there appears no reason
a /priori should be in conformity with the simple law
of aberration.
Accordingly Dr Young, to whom mainly we owe
the revival of the theory of undulations which took
place about the beginning of this century, supposed
that instead of the earth's pushing the ether out of its
way, it allowed it to pass freely through its substance,
.8000 miles though it be in thickness, far more freely
than a grave of trees transmits the wind ; and that in
consequence of this perfect freedom of passage, the
ether outside the earth's surface was not disturbed by
the earth's motion, nor consequently the undulations
passing through it.
Now startling as is this suppositiofi, and contrary
to all that we should have anticipated, we cannot say
that it must be rejected. For wq must remember
that we have 110 direct evidence even of the existence
of an ether ; it is not directly recognizable by any of
pur senses ; its properties may be, and doubtless are^
24 THE NATURE OF LIGHT.
very different from those of ponderable matter, and
we must be content to learn them by degrees, as they
may be revealed by the study of the phenomena
which are referable to actions of the ether. Never-
theless we are not absolutely driven to accept Dr
Young's hypothesis; for there is as I have shown
another way in which the law of aberration may be
obtained; a way which though not free from diffi-
culties exempts us from the necessity of supposing
that the earth in its motion through the ether allows
the ether to" pass through it with absolute freedom.
At this point it may be well to pause for a
moment and consider the probabilities in favour of
the two hypotheses. The existence of rays and
shadows seems perfectly simple according to the
theory of emissions ; as far as we have gone it pre-
sents a serious difficulty on the theory of undulations.
The laws of reflection and refraction leave little
tof choose between the two. In one respect indeed
the theory of undulations has the advantage ; for it
indicates that there ought to be a partition of the
incident light into a portion reflected and a portion
refracted, whereas on the other we should rather have
expected that the light would have either been re-
flected or refracted. This advantage is however of
no great weight, for it would not be difficult to frame
plausible hypotheses in the theory of emission which
COMPARISON OF THE TWO THEORIES. 2$
would lead to a partition. As regards aberration, the
corpuscular theory has a decided advantage, for on
it the explanation of the phenomenon is perfectly
simple, whereas according to the theory of undula-
tions all we can say is that it is not inexplicable.
The balance on the whole seems to lean towards
the side of the corpuscular theory. And yet that
theory is now altogether exploded, and the rival
theory is established on so firm a basis that no one
who has studied the subject can doubt that the second
of the two modes of conception with which we started
expresses the truth, and that light really consists of a
change of state propagated from point to point in a
medium existing between the luminous body and that
which the light affects.
It may be said, If the former theory is now-a-days
exploded, why dwell on it at all ? Yet surely the
subject is of more than purely historical interest. It
teaches lessons for our future guidance in the pursuit
of truth. It shows that we are not to expect to
evolve the system of nature out of the depths of our
inner consciousness, but to follow the painstaking
inductive method of studying the phenomena pre-
sented to us, and be content gradually to learn new
laws and properties of natural objects. It shows that
we are not to be disheartened by some preliminary
difficulties from giving a patient hearing to a hypo-
26 THE NATURE OF LIGHT,
thesis of fair promise, assuming of course that those
difficulties are not of the nature of contradictions
between the results of observation or experiment and
conclusions certainly deducible from the hypothesis
on trial. It shows that we are not to attach undue
importance to great nanies, but to investigate in an
unbiased manner the facts which lie open to our
examination.
I now conie to other classes of phenomena with
respect to the explanation of which there is the widest
possible difference between the two hitherto rival
theories respecting the nature of light. We are
all familiar with the vivid colours of soap bubbles,
colours which are exhibited in the case of transparent
solid plates or liquid films which are excessively thin,
or of very thin plates of air contained between two
surfaces of glass which are in contact, or almost in
contact, Trt tjiw puiwi . It ts te Nc^ ion that we owe
the first investigation of the laws of these " colours of
thin plates " as they are called. By placing a convex
lens of small curvature in contact with a plane piece
of glass, we obtain a separating plate or film of air
the thickness of which vanishes at the point of contact,
and increases very slowly at first on receding from it.
In this case the colours are arranged in circles round
the point of contact, the rings forming annuli of
increasing diameter but decreasing width as we
COLOURS OF THIN PLATES. 2^
recede fronl the centre outwards. The centre is dark ;
and when the incident light is white, on going out-
wards about seven alternations can be traced, after
which the field is sensibly of uniform illumination
and free from colour. The squares of the diameters
of the rings are found to increase in arithmetic
progression in passing from ring to ring.
When instead of using white light the system of
the rings is illuminated by the colours of a pure
^ectrum, a vast number of rings is seen ; in fact, they
go on till from the increasing narrowness of the annuli
they become too fine to be seen. In this case the
colour naturally reitfttios the same, being that of the
part of the spectrum that b 44sed to illuminate the
glasses. The $cale of the system l!hwjges greatly
with the colour, decreasing from the red to the vlotat.
The scale of the system depends very greatly
upon the curvature of the lens ; and to form the rings
on a large scale, which is convenient for examination,
it is necessary to use a lens of small curvature. The
thickness of the interposed plate of air where any ring
is formed can be obtained by an easy calculatioo
from the diameter of the ring and the radius of
curvature of the lens, both which can be measured.
When this is done it is found that a given ring is
always formed where the plate has a given thickness.
If the interposed medium be water instead of air.
28 THE NATURE OF LIGHT.
or generally any transparent fluid, the scale of the
rings is diminished. It is found that the square of
the diameter of a given ring varies inversely as the
refractive index of the interposed liquid.
As my object is not to give a complete account of
the phenomena of the rings, much less a complete
explanation of the phenomena, I shall dwell no further
on the appearances which the rings present under
different circumstances, the features I have already de-
scribed being sufficient for my purpose, which is to give
a fair idea of the evidence on which rests that theory
as to the nature of light which we shall be led to adopt.
Newton endeavoured to account for the various
phenomena of thin plates by his celebrated theory of
fits of easy reflection and transmission. We have seen
that the existence of both reflection and refraction is a
difficulty in the theory of emission which has in some
way to be accounted for. It will not do to suppose
that there are two permanently distinct kinds of light,
of which one, when the light falls at a given inclination
on a given substance, is always reflected and the other
always transmitted, for if either the reflected or the
transmitted beam be allowed to fall at the same angle
on the same substance, it is divided into a reflected
and a transmitted beam. We must therefore suppose,
even independently of the phenomena of thin plates,
•that the same particles of light are sometimes in a
NEWTON'S THEORY OF FITS. 29
condition to be reflected and sometimes in a condition
to be transmitted : and we have only further to postu-
late that these changes of state, whatever may be
their nature, take place with a regular periodicity in
order apparently to account for the phenomena of
thin plates, at least if we restrict ourselves to the case
of a perpendicular incidence on a plate of given kind,
such as a plate of air between two surfaces of glass.
For all the light which is transmitted by the first
surface must be in a fit of easy transmission which it
does not at once lose, so that if it falls immediately on
the second surface it is transmitted, and therefore the
central spot looks comparatively black. The same
must be the case where the distance between the
surfaces is equal to the length of a fit, or 2, 3, &c.
times the leng^ of a fit; and for intermediate
thicknesses of the plate, corresponding to intermediate
distances from the point of contact, the effect will be
intermediate, and there will be more or less reflection,
which will be greatest for thicknesses exactly half
way between the critical thicknesses above mentioned.
But tempting as this theory at first sight appears,
though if it be true it must be left to subsequent
research to indicate what that periodic element in
relation to the particles of light can possibly be
which shows itself by an alternate capacity for
reflection and refraction, it fails completely to account
36 TH£ NATURE OF LIGHT.
for the other features of the phenomenon, some of
which I have mentioned. We should have expected
beforehand that the length of a fit wbuld have been
independent of the angle of incidence ; and when we
learn that to reconcile theory and observation we must
suppose it to vary as the secant of the angle of inci-
dence, we see no way of accounting for such a law.
Again, as to the effect of a change of medium, the
most natural supposition to make would be that the
constant element of periodicity which characterises
light of any particular refrangibility is a constant
periodic time. Now the explanation of the law of
refraction according to the theory of emission requires
us to suppose that light travels faster in refracting
media than in vacuo, in the ratio of the refractive
index to unity. We might have expected accordingly
that the length of a fit in water would be greater thaa
in air in that ratio. We have seen however that it is
less in the inverse ratio. We are unable to frame any
plausible hypothesis, on the theory of emission, why
it should be so.
Accordingly the theory, if such it can be called,
consists merely ^ of a . set of incoherent laws, not
indicated bef(arehand' by theory, not even falling
in with it after they have been pointed out by obser-
vation, and it has accordingly nothing about it which
seems to bear the stamp of truth.
INSUFFICIENCY OF THE THEORY, 3I
Nor is this all. Even as regards the formatioa of
■the rings at a perpendicular Incidence, where at first
sight the theory appears to be most successful, it leads
to a conclusion which is belied by observation. Accord-
ing to this theory, the office of the first surface of the
plate is solely one of sifting, by reflecting back those
particles of light which are in a fit of reflection, and
thereby preparing the way for the alternate transmis-
sion and reflection of the particles at the second
surface. There should therefore be as much light
feflected at the first surface as if the second glass were
away altogether, and therefore the dark rings should
be only comparatively dark. The experiment may
be easily and successfully tried with homogeneous
light, such as that of a spirit-lamp with salt on the
wick, and it is found that the dark rings are decidedly
darker ; in fact as to sense apparently black.
LECTURE II.
Interference — Explanation of the colours of thin plates
ajforded by the theory of Undulations — Diffraction,
In my last lecture I pointed out the insufficiency
of the theory of emission to account for the various
phenomena of the colours of thin plates. Let us now-
see whether the theory of undulations lends itself to-
an explanation. In the first place the element of
periodicity, instead of being wholly extraneous to
the fundamental idea, and hardly if at all to be re-
conciled with it even when suggested by phenomena,
is one naturally, almost inevitably, involved in the
fundamental conception. I say, almost inevitably;
for a set of undulations might consist of a succession
of isolated pulses following one another in a wholly
irregular manner ; but the analogy of sound would
make it far more likely a priori that they should
form a series of regularly periodic disturbances;
and the supposition that such is their character
therefore harmonizes perfectly with what we should
have expected beforehand.
INTERFERENCE* 33
Supposing then that the undulations we have to
deal with are regularly periodic, can we on the undu-
latory theory give any account of the alternations of
light and darkness which we observe in Newton's rings ?
The explanation which this theory affords is
based on a very simple and very general dynamical
principle, of very wide application, called the principle
of the superposition of small motions. For the sake
of those who may not have much attended to dy-
namics, I will endeavour to give some idea of what
this principle means.
Suppose a stone thrown into still water. It pro-
duces as we know a, series of small waves, which
spread out in the form of circles from the place of
disturbance. What passes outwards is, not the ma-
terial particles of the water, but a certain state of
things. If we observe a minute floating body, it is
seen to retain its average position, and merely to
move very slightly backwards and forwards, up and
down. So far, we have merely a visible illustration
of the progress of an undulation, differing it. is true
from those belonging to sound or light in the fact
that it is only in the neighbourhood of a particular
surface that the disturbance is sensible, which does
not however prevent it from forming a useful illustra-
tion for those to whom the conception may be new.
But now instead of a single stone, suppose that
S. 3
34 THE NATURE OF LIGHT,
there are two similar stones thrown in simultaneously
at a little distance apart. Each will give rise to a
series of circular waves which at first will be distinct,
each diverging from its own centre, but not yet
having reached one another. But presently the waves
from the one centre will invade the region occupied
by those from the other. What will then take place ?
According to theory, each disturbance will find the
mass in which it is being propagated under as nearly
as possible the same conditions, so far as itself is
concerned, as if the other disturbance did not exist.
The consequence is that any particle of the mass will
be as much displaced from its mean position as if
the other disturbance did not exist, and its actual
place will therefore be found by compounding, as it
is called, the displacements due to the two dis-
turbances taken separately. Accordingly where a
ridge due to one of the disturbances coincides in
position with a ridge due to the other, we have an
elevation of double height, supposing we choose a
place where the intensities of the disturbances due to
the two sources are the same ; but where a ridge due
to one falls in with a trough due to the other, we
have neither elevation nor depression, but the water
is found at its natural level.
Now if there be any truth in the theory of undula-
tions, something of the same kind must take place
INTERFERENCE. ^S
With light. If we have two sets of disturbances
always exactly alike, then when the conditions are
such that the two disturbances separately considered
take place always in opposite directions, being super-
posed they simply produce a disturbance nil, whereas
when the directions agree they produce a disturbance
of greater amount than either separately. And if
light consist of such a disturbance in the ether, then
in the former case we ought to have no light, whereas
in the latter the light ought to be greater than if the
one set of disturbances alone existed. And if the
two sets of disturbances^ while still in other respects
alike, differed in amplitude in a constant ratio, the
only difference that would make in the result would
be that the light would not vanish at the minima.
But it must be particularly remarked that in order
that this neutralization should always take place in
the same way at the same place, it is essential that
the two sets of disturbances should always agree as
to their times of starting, or differ, if they do differ,
by a perfectly constant quantity. For if one were
half an undulation ahead of the other, that would
make all the difference whether the two disturbances
strengthened or neutralized each other : and if the
relative times of starting varied irregularly a vast
number of times in a second, we should have at a
given place neutralization and cooperation succeeding
3—2
3$ THE NATURE OF LIGHT.
one another so rapidly that nothing but the meart
effect would be perceived, and that, as may be shown,
would be simply the sum of the mean effects taken
separately. Now if the disturbances came from two
independent sources, such as two different portions of
a flame, the relative starting points of the two would
be purely casual, .and no fixed and permanent
neutralization would be to be expected. And obser-
vation shows that none of those alternations of light
and shade which on the theory of undulations we
refer to interference are manifested unless the two
interfering streams of light have come originally from
the same source, having subsequently pursued slightly
different paths.
Let us now see how these principles apply to the
explanation of Newton's rings. If we consider a
small portion of the thin plate of air by reflection
from which they are seen, we perceive that there are
two reflecting surfaces near one another, and conse^
quently two reflected streams, one reflected from the
upper surface of the plate of air, that is, internally in
the upper glass, and the pther reflected from the
under surface of the plate of air, that is, from the
upper surface of the under glass. These are it is true
accompanied by other streams which have been
reflected backwards and forwards internally in the
plate, so that the total number of reflections in these
EXPLANATION OF NEWTON'S RINGS. 3/
streams is 3, $, 7, 9...; but these streams, being
usually comparatively weak, may in a general ex-
planation be left out of consideration. Now the
second of these streams has had to travel a very
little further than the first. In the simplest case, to
which we may confine ourselves for the present, that
of a perpendicular incidence, the excess of length of
path of the second stream is evidently just double
the thickness of the plate of air, and varies accordingly
from point to point of the field of view, the thickness
increasing slowly at first and afterwards rapidly as
we recede from the point where the lenses are in
contact. Close to the point of contact, the second
stream is only imperceptibly behind the first, and the
two might be expected to be in accordance, that is,
to agitate the ether in the same direction, and there-
fore to strengthen one another. As we take a point
further outwards from the point of contact, the retar-
dation increases, and when it becomes half the length
of a wave the two would be in opposition, that is, one
would agitate the ether in a way just opposite to
the other, and therefore, supposing the intensities of
the two the same, as would nearly if not exactly be
the case, they would neutralize each other, and dark-
ness would be the result. And as the thickness of
the plate of air between the two glasses varies as the
square of the distance from the point of contact, the
38 THE NATURE OF LIGHT.
law of increase of the rings fpr any one kind of light
as the order of the ring increases follows at once, and
moreover the law that under different circumstances
as to curvature of the glasses the same ring is always
formed where the thickness of the plate is the same.
But there is one mafked point of contrast between
the results of theory, so far as I have yet explained it,
and observation, namely, that we have been led to
expect a maximum of brightness where the paths of
the two streams are the same, that is close to the
point of contact, or where they differ by one, two, or
a complete number of undulations, and a maximum
of darkness if not absolute blackness where the
difference is an odd number of half undulations.
This would give the places of light and shade exactly
reversed as compared with observation, which would
show one of .two things, either that the theory must
be rejected, or that some circumstance has been over-
looked which, had it been taken into account, would
have made the theoretical result right in this respect.
Now the reflections which the two streams re-
spectively undergo take place under very different
circumstances. The first stream is reflected internally
in glass when the light, which had previously been
travelling in the glass of the upper lens, arrives at the
under surface of the glass, or upper surface of the
interposed plate of air, the second is reflected back
EXPLANATION OF NEWTON'S RINGS. 39
into air at the upper surface of the under lens. As
the two reflections take place under different, in some
respects opposite, circumstances, there seems nothing
unlikely a priori in the supposition that the signs of
the reflected vibration should be opposite in the two
cases. Dynamical analogies are not far to seek ; for
example, we know that when sound travelling along
a pipe meets a closed end, it is reflected in such a
manner that condensation in the reflected answers to
condensation in the incident, and rarefaction to rare-
faction; but when it is reflected, as reflected it is,
from the open end of a tube, rarefaction answers to
condensation and condensation to rarefaction. And
this theoretical conclusion as to the opposition of
signs in the two cases, so probable from analogy, is
converted into a certainty by the application of a
simple dynamical law of great generality, which may
be called the law of reversion. Hence then the
occurrence and features of the rings at a perpendicu-
lar incidence, for any one kind of light, are on the
undulatory theory matters of pure prediction.
Next consider the effect of inclination. It follows
from a very easy calculation that the effect of the
thickness of the plate of air a;t any inclination in
producing retardation in the stream reflected from
the second surface of the plate, relatively to the
stream reflected from the first surface, is the same
40 rut NATURE OF LIGHT.
as it would be at £l perpendicular incidence for a
thickness smaller in the proportion of the cosine of
the inclination of the light while in the plate of air to
unity, or, which is the same thing in the case of a
lens with nearly parallel surfaces for the upper glass^
of the cosine of the angle of incidence on the first
surface to unity. Hence follows at once the simple
law of dilatation of the rings on increasing the angle
of incidence, namely, that the square of the diameter
of any ring varies as the secant of the inclination on
the first surface* Of this law, as we have seen, the
theory of emissions could give no account.
Again, the effect of the substitution of water for
air between the lenses in causing the rings to con-
tract, and the law of their contraction already men-
tioned, follow immediately on this theory from first
principles, since the explanation of refraction on the
theory of undulations necessitates the supposition
that light travels more slowly in refracting media
than in vacuum, in the proportion of the refractive
index to unity.
In short, the theory completely explains the phe-
nomena of the rings seen by reflection. And this is
true even as regards the more minute features, into
which I have refrained from entering. The New-
tonian "fit" at a perpendicular incidence expresses
half the length of a wave ; and as the scale of the
EXPLANATION OF THE TRANSMITTED RINGS. 4I
rings decreases from the red to the blue, and accord-
ingly as the refrangibility of the light increases, we
learn that the variable element in light which corre-
sponds to a change of refrangibility and change of
colour must be the wave-length in vaaio^ or, what
comes to nearly the same if not exactly the same
thing, the periodic time. The compound tints of the
rings are explained here as in all other optical phe-
nomena, whatever theory of light we may adopt, by
the superposition of the ring-systems corresponding
to the different kinds of light of which white light
consists, which are on different scales as to size ;
and the fact that not more than about seven rings are
seen with white light merely depends on the over-
lapping of the rings of high orders corresponding to
the different colours.
I have hitherto said nothing about the system of
rings in the transmitted light, which are complemen-
tary in character to the rings seen by reflection, but
far less vivid, resembling in fact a vivid system com-
plementary in character to the reflected system, over-
laid by a comparatively large quantity of uniform
white light. In nearly every respect the theory of
these is analogous to that of the reflected system, so
that whatever theory explains the one can hardly fail
to explain the other. There is just one feature the
explanation of which involves considerations into
!1
•I
I
42 THE NATURE OF LIGHT.
which I have not entered, and to this I will confine
myself.
The transmitted system, according to the expla-
nation afforded by the theory of undulations, depends
on the interference of two streams of light, one
passing right through the plate of air comprised
between the lenses, and the other following it after
two reflections in air at the adjacent surfaces of
the glasses. These are associated with other por-
tions which have been reflected 4, 6... or any even
number of times ; but these, being usually compara-
tively weak, may in a general explanation be disre-
garded.
Now when light is incident perpendicularly, or
nearly so, on the surface of crown glass, about 4 per
cent of the incident light is reflected, and the rest
enters the glass. The intensity of light once reflected
in this manner being thus only the ^^th of the in-
tensity of the original, the intensity of light twice
reflected will be only the ^th of that, or the ^^^ of
the original. Now as the light which passes through
one surface loses only 4 per cent by reflection, the
light which passes through the two surfaces of the
plate still retains the 0*96* or 0-9216 of its original
intensity; so that the twice reflected light has an
intensity only the ^tfa of the direct, hardly more
than one-sixth per cent How then, it might be said.
EXPLANATION OF THE TRANSMITTED RINGS. 43
could SO small an addition or subtraction of light be
perceptible at all, and so produce in homogeneous
light differences of intensity, and with white light
changes of colour, which though not it is true by any
means so strikii^ as in the reflected system of rings
are nevertheless very evident, and demand far greater
differences of intensity than that ?
The explanation of this paradox lies in a con-
sideration of the relation between intensity and am-
plitude of vibration. If light consists in a disturbance
of a subtile medium, or ether, then the greater be
the disturbance, other circumstances being the same,
the stronger must be the light. But supposing the
amplitude of excursion of the ether to be doubled,
trebled... is the intensity of the 'light doubled, trebled
... or if not, in what other proportion is it increased ?
Now a number of different considerations lead
decisively and independently to the same conclusion,
namely, that the intensity is to be measured by the
square of the amplitude of excursion. Hence if the
amplitude of excursion to and fro of the ether is
increased in the proportion of i to 2, 3..., the inten-
sity of the light is increased in the proportion of i to
4,9...
Suppose now that two disturbances from the same
source, and following nearly the same path, have a, b
for the coefficients of excursion due to them sepa-
44 THE NATURE OF LIGHT.
rately; when acting together the coefficients of ex-
cursion will fluctuate between the limits a + 6 and
a — 6 according as the phases are in agreement or in
opposition* Hence whereas the intensities of the two
separately will be in the ratio of a^ to 6\ the maximum
and minimum intensities due to the compound dis-
turbance will be proportional to (a + 6y and (a — by.
Suppose now the first disturbance to be very
much greater than the second, then a will be very
much greater than 6. Hence whereas the sum or
difference of the intensities of the two streams would
be got by adding or subtracting ^' to or from a^, the
maximum and minimum intensities of the compound
disturbance will be got very nearly by adding or sub-
tracting 2ad, a quantity which is greater than the
former in the proportion of 2a to 6. Thus with the
numerical values just mentioned, which are applicable
to Newton's rings at a perpendicular incidence, if we
take the coefficient of vibration and the intensity of
the stronger stream each for the unit of their respec-
tive kinds, the coefficient of vibration of the weaker
stream will be ^ and the intensity ^ nearly, where-
as the maximum and minimum intensities of the
compound stream will be i ± ^ nearly, and the differ-
ence between them will be as great as ^.
In the particular case of Newton's rings, the
weaker stream is not readily viewed apart; but in
PIFFRACTION FRINGES. 45
certain experiment^ of diffraction, ^ subject that
will be touched on by and by, the two streams lend
themselves readily to separate observation, and the
occurrence of distinct fringes of interference theo-^
retically referable to an invisible agent — invisible be^
cause too faint to be seen — is not a little paradoxical
in appearance.
It appears then that the fundamental hypotheses
pf the undulatory theory suffice to account in the
most complete manner for the phenomena of New-
ton's rings, and the colours of thin plates in general,
without making any fresh assumption whatsoever.
It is to Dr Young that we owe the explanation of
these colours on the theory of undulations, an expla-
nation given at a time when any other theory than
the corpuscular could hardly gain a hearing ; and to
him also we owe the first direct experiment proving
that (pertain fringes which connect themselves by
numerical relations with Newton's rings are incon-
testably due tp interference.
As introductory to this experiment, it will be
convenient to mention another phenomenon which
forces itself upon the notice of t|ie observer simulta-
neously with that with which we are more immedi-
ately concerned, and which therefore it is desirable to
be able at once to refer to its proper place, besides
tbftt at a more advanced stage of our study of the
46 THE NATURE OF LIGHT.
subject it will be found to be of very great impor-'
tance.
Suppose that the sun's light is reflected hori-
zontally into a darkened room, passing through a
very small hole in the shutter, or what is more con-
venient through a lens of short focus. Let the light
be allowed to fall on an opaque screen at the distance
say of a few feet from the luminous point, the screen
being terminated by a straight edge, suppose vertical.
Let the light passing the edge of the first screen be
received on a white vertical screen which we may
suppose a few feet further off from the luminous
point According to geometrical optics, if we project
the edge of the opaque screen on to the receiving
screen, by straight lines drawn from the luminous
point, all to the illuminated, suppose the right-hand,
side of the projection we shall have uniform illumina-
tion, the same as if the opaque screen were away,
while all to the left of it we shall have darkness.
According to observation, there is no such abrupt
transition on the receiving screen from uniform dark-
ness to uniform brightness. The illumination in-
creases continuously, though rapidly. The illumi-
nation begins to be sensible before we reach the
geometrical shadow, or projection of the straight
edge, where it is still considerably feebler than the full
illumination at a distance on the right On going in
•DIFFRACTION FRINGES. 47
a right-hand direction from the geometrical shadow
the illumination rapidly increases, and actually be-
comes considerably greater than the full illumination
at a distance. It then decreases to a minimum,
increases to a maximum, and so on, the maxima and
minima differing less and less, by excess and defect
respectively, from the illumination at a distance, and
gpradually occurring in more rapid succession, till they
become insensible. Three such bands can usually
be traced before the illumination becomes sensibly
uniform. With white light the scale of the bands,
and of their distances from the geometrical shadow,
changes as usual from colour to colour, decreasing
from the red to the blue. The appearance is the
isame at all distances of the two screens from the
luminous point, the scale, merely, of the system vary-
ing according to circumstances, and likewise the
smallness demanded in the source of light in order
that the bands may not be confused. From the
constant character of these bands we readily recog^nise
them in experiments in which they appear associated
with other phenomena.
Suppose now that instead of the opaque screen
extending indefinitely on one side, the light is inter-
cepted by a narrow slip, a knitting-needle, or any-
thing of the kind. The shadow is bounded on both
sides externally by fringes of the character of those
48 THE NATURE OF LIGHT.
just described, and which accordingly we must attri-:
bute to the same cause, referring the right-hand set
to the light which passed to the right of the obstacle,
acting independently of that which passed to the left,
and similarly as regards the external fringes of the
left, But besides these the shadow itself is occupied
by another set of coloured fringes, finer usually than
the former, and unlike them of equal width through-
out. They may be viewed through an eye-lens ; and
thereby magnified. If the screen be semi-transparent,
we may view them with the lens from behind, and
now if we take away the screen altogether, using
nothing but the lens, and receiving the light directly
into the eye, we see them as before. But now they
are much brighter, since the light is no longer scat-
tered in all directions by a screen, so that we can
afford to use a narrower source of light, suppose a
lens of shorter focus in the window ; and having the
narrower source we may use a wider opaque slip
without the fringes getting confused. Under these
circumstances the system of internal fringes occupies
only the middle portion of the shadow, being well
separated from the external fringes on both sides.
The very centre of the shadow is bright for all the
colours of the spectrum, and the middle bright band
is accordingly white, except just at the edges, where
it is slightly reddish, but after that the bands right
t)IFFRACTION FRINGES. 49
and left soon become coloured, on account of the
difference of scale for the different colours.
Now what account tan we give of the formation
of these internal fringes on the theory of undulations?
We have seen that when light passes by an opaque
screen, it does not at once become insensible within
the limits of the geometrical shadow ; a little lightj
bends round the edge into the darkness, enough to
produce a feeble and rapidly decreasing illumination
on a screen placed to receive it. This " inflexion '^ of
light is a fact, account for it as we will : and if light
consists of undulations, the analogy of those undu-
lations which we can directly examine would lead us
to infer that light must be inflected into a shadow.
Indeed the grand original difficulty which for so long
a time prevented the reception of the theory of
undulations was that of accounting for the com-
parative absence of inflexion ; in other words, for the
existence of rays and the sharpness of shadows.
Admitting this small inflexion as a fact, we see that
at any rate we can not be far wrong in supposing the
bending to take place close to the edge of the
obstacle. On this supposition, the length of path of
the inflected stream in travelling from the luminous
point to the point of the field, or focal plane of the
eye-lens, where we seek the illuiiiination, will equal
the path from the luminous point to the edge of the
S, 4
5Q THE NATURE OF LIGHT.
obstacle, //^j" the distance from thence to the point in
the field. The difference of paths for the two in-
flected streams which reach the same point of the
field is accordingly easily found, especially as we are
only concerned with points lying but a very small
distance from the plane passing through the luminous
point and the middle of the obstacle, or say the
central plane. The difference of path vanishes at the
central plane, where accordingly we have a maximum
of brightness, and On receding in a lateral direction
from the central plane the difference of path changes
in proportion to the lateral distance, and accordingly
it is equal to i, 2, 3... wave-lengths for a series of
equidistant straight lines parallel to that in which the
central plane cuts the field. These lines are what
ought according to theory to be the middle lines of
bright fringes, and lines midway between them ought
to be the middle lines of dark bands separating the
fringes. The theoretical breadth of a fringe, being
sensibly independent of the distance of the luminous
point, is connected with the wave-length by a very
simple formula, involving only the distance from the
opaque slip to the screen on which the light is received
and the breadth of the slip, both of which can easily be
measured. On the other hand, the fringes are actually
seen, and their breadths can be measured. Com-
paring the theoretical and observed breadth of a
DIFFRACTION FRINGES. 5 1
fringe, we obtain the value of the quantity which if
the theory be true expresses the length of a wave.
On comparing this with the measure obtained from
Newton's rings, we obtain identically the same value
within the limits of errors of observation.
This numerical relation indicates that the alter-
nation of light and dark in these two different pheno-
mena is referable to a common cause, whatever that
may be. Newton endeavoured to explain the rings
which go by his name by the theory of fits of easy
reflection and transmission. We have seen that this
theory failed to account for the dilatation of the rings
produced by increasing the angle of incidence, and
for their contraction produced by the substitution of
water for air as the interposed medium. Still, it gives
correctly the law of increase of the radii of the rings
at a perpendicular incidence as the order increases,
and the law connecting the scale with the curvatures
of the lenses. Now confining ourselves to the case of
a perpendicular incidence, where the theory of fits is
most successful, we may notice one radical difference
between the explanations offered by the theory of fits
and the theory of undulations. According to the
former, the office of the first surface of the thin plate
is simply one of sifting, and it is by reflection or non-
reflection from the second surface that the rings are
formed. According to the theory of undulations on
4—2
52 THE NATURE OK LIGHT.
the other hand, there is no sifting at all : the light
reflected from and the light transmitted by the first
surface have both one and the other just the same
properties as the incident light, and it is by the
simultaneous working of the light reflected froiii the
upper and that reflected from the under surface that
the alternations of illumination are produced. Now
in the experiment of the internal fringes, there is
absolutely nothing to sift the light, and yet we get
alternations of light and darkness as in Newton'sl
rings, and what is more are conducted to the very
same measurable length, clearly representing some-
thing inherent in the nature of light, which according
to the theory of undulations is simply the length of a
wave, the conception of which is radically involved
in the fundamental points of the theory. We can
hardly refuse to admit that the alternations of light
and dark witnessed in these two phenomena are
really due to interference ; to the simultaneous
working of two portions of light.
This conclusion was converted we may say into a
certainty by a celebrated experiment of Dr Young's
on the internal fringes. He showed that if a small
opaque screen were placed so as to intercept the light
going to fall on one side of the narrow slip, or else
which had already passed it, in either case the central
fringes disappeared as well as the external fringes on
young's experiment op interference. 53
the same side of the slip. And if a plate of glass
were substituted for the opaque screen the intertial
fringes disappeared as before, but now the external
fringes were seen on both sides. It is clear therefore
that the internal fringes are really due to the joint
working of the two portions of light inflected in
passing the two edges, while as regards the external,
those which appear on the right and left are inde-
pendently produced by the light which passes on the
right and left respectively of the opaque slip. The
disappearance of the internal fringes occasioned by
the interposition of a piece of glass on one side only
of the opaque slip is explained in the same way as
the non-exhibition of Newton's rings, when white
light IS used, outside a very moderate number sur-
rounding the point of contact of the glasses.
After what precedes, the reality of the interference
of light might well be taken as established. It is to
be noted however that in the theory of the last
experiment we have had to take for granted the in-
flexion of light. It is true that the fundamental con-
ceptions of the theory of undulations lead us to expect
inflexion, the difficulty being rather to explain howthere
is so little. We have not however as yet seen how
the determination of the inflexion is to be brought
within the domain of theory, and to that extent we
have been working in a field not yet fully explorecj^-
54 THE NATURE OF LIGHT.
It IS to Fresnel that we owe the first experiment of
interference in which there is neither a thin plate, the
first surface of which might according to Newton's
views have exercised a sifting action on the light, nor
anything unusual, such for example as inflexion,
occurring in the progress of the light, but in which
the two portions of light that interfere are simply
regularly reflected or refracted as the case may be.
This object was accomplished by Fresnel in two
ways, by reflection and by refraction: by a pair of
interference mirrors, and by an interference prism,
which is a prism with a very obtuse angle, such as 179®.
It will be sufficient to mention the former method.
Let two plane mirrors be procured, such as two
pieces of plate glass, blackened on the back, each
mirror being bounded by a straight edge. Let them
be mounted so that the straight edges are close
together, and the planes of the mirrors are nearly but
not quite continuations of each other ; the planes of
the faces making with each other a very obtuse
angle, suppose only a fraction of a degree less than
180®, the concavity being on the side of the reflecting
faces. Great care must be taken that neither mirror
juts out above the other where they meet along the
straight edges, which may be ascertained by passing
the finger lightly across the junction. Let the sun's
rays be reflected into a darkened room, and brought
INTERFEK,ENCE SHOWN BY TWO MIRRORS. 55
to a point, or what may be regarded as such, by a lens
of short focus. Let the light progeeding from the
luminous point be received, say at the distance of a
few feet, on the pair of mirrors. According to geo*
metrical optics, the light reflected from each mirror
will proceed after reflection as if it came from the
virtual image of the point in the mirror. If each
mirror be projected into space by lines drawn from
the virtual image belonging to it, we see that there is
a narrow wedge of space within which both reflected
streams mix. If the light be received on a screen
there will be two illuminated areas corresponding to
these two projections respectively, and a narrow ijaore
highly illuminated band where the two overlap, cor^
responding in fact to a section, by the plane of the
screen, of the wedge above spoken of. If this doubly
bright portion of the field be more carefully scru-
tinized, by removing the screen and receiving the
light directly into the eye through an eye-lens, we
see the field marked on both sides by the usual
external fringes at the boundary of an illuminated
field. But besides these we see, running parallel to
these along the middle of the field, a set of sharply
defined, and commonly much narrower fringes, which
as usual are on a different scale for the different
colours^ coarser for the red, finer for the blue. These
are quite different in appearance from the compara-
56 THE NATURE OF LIGHT.
tively vague external fringes which are seen at both
sides of the field. And if any suspicion were enter-
tained that after all these sharply defined fringes, sad
to be due to the interference of two regularly reflected
streams, were really connected with the external
fringes, their complete independence would be shovn
by a very simple modification of the experimett.
Adjust the mirrors so that one shall jut out a vay
little above the other towards one end of the line of
junction, and the other towards the other, this will be
sufficient to make the line of intersection of the planes
of the mirrors altogether oblique to the line of junc-
tion. The region of space within which the two
streams mix remains as before, and the external
fringes which bound it on the two sides, but the
sharply defined fringes which before ran along the
middle of the doubly bright region, being parallel to
the line of intersection of the planes of the mirrors,
are now altogether oblique to the line of junction, and
accordingly inclined at a considerable angle to the
external fringes. When the sharply defined fringes
begin to run out of the doubly bright portion of the
field, they and the external fringes begin to modify
one another, but under the conditions which usually
prevail, and at any rate are easily obtained, the
former pursue for a long way their oblique course
quite undisturbed.
INTERFERENCE BELONGS TO LIGHT. '57
It IS proved therefore to absolute demonstration
that the property of interference is one essentially
belonging to h'ght from its very nature* Two lights
of the same kind, that is, of the same refrangibility,
from the same source do really strengthen or oppose
each other, in the latter case producing darkness if the
intensities are equal, according as their lengths of
path from the source to where they mix are the same
or differ by a multiple of a certain length depending
on the nature of the light, or as they differ by an odd
multiple of half that constant. And if part of the
path lies in some refracting medium, as water, instead
of air, it is equivalent, so far as interference is con-
cerned, to a path in air greater in the proportion of
the refractive index to unity, and which accordingly
would take exactly the same time to be travelled over
according to the theory of undulations, since according
to that theory the velocity of propagation in media is
less than in vacuo in the proportion of unity to the
refractive index.
This fundamental constant, which according to
the undulatory theory expresses the length of a wave,
may be determined more or less accurately by any of
the instances of interference above mentioned ; though
the progress of our knowledge has furnished us with
methods of determining it of still greater exactness.
It increases as we have seen, and that considerably,
58 THE NATURE OF LIGHT.
soniething like in the proportion of 2 to 3, in
passing from the blue to the red. As to its absolute
value, it will be sufficient to say that for rays of mean
refrangibility we may take it in round numbers at the
^^f^th part of an inch*
We have seen with what admirable simplicity the
theory of undulations explains the various phenomena,
in all their details, which have been mentioned as
referable to interference. And yet the grand original
difficulty, that of explaining the existence of rays and
shadows, has been left untouched, or received at most
only a lame explanation. Yet if the theory be true it
ought to be capable of accounting for these phenomena
as well as for those, in some respects simpler in
character, which have been so successfully referred to
interference.
It is remarkable that it was not till the study
of the theory of light had made great progress,
subsequently to the revival of the undulatory theory
about the beginning of the present century, that
the elementary phenomena of rays and shadows
received their full explanation; and yet, once that
explanation is propounded, it is seen to involve
nothing more than the very elements of the theory of
undulations ; to be in fact nothing more than might
have been foreseen from the beginning had the human
race been sufficiently acute. The history of thp
RAYS ARE A PHENOMENON OF DIFFRACTION. 59
explanation compared with our present knowledge
affords a remarkable example of the manner in which
we start on our course of investigation by mounting
on the shoulders of our predecessors ; and so it may
very likely be in the future that things that appear to
us mysterious, and which we labour hard to explain,
will to our successors seem so simple that they will
wonder why we did not find them out
I have mentioned the external fringes seen on the
illuminated side of the geometrical projection of a
straight edge bounding an opaque body exposed to
light coming from a luminous point, which is taken as
the point of projection. This phenomenon is modified
in a great variety of ways according to the outline of
the opaque body. It may for instance be a screen
containing one or more apertures. Suppose the
aperture circular. If the circle be moderately large,
and the light be received on a screen beyond, we have
a circular illuminated patch corresponding nearly with
the projection of the hole, which is seen to be fringed
within its boundary by fringes resembling the external
fringes spoken of just now. If the size of the hole be
diminished, or the distance of the receiving screen
increased, which produces a similar effect, the fringes
invade what had previously been the uniformly
illuminated area corresponding to the projection of
those, portions of the hole which are at a little distance
6o THE NATURE OF LIGHT;
from its edge ; and after a very curious and complicated
set of changes we are ultimately, when the hole is
made very small, left with a circular patch of rather
weak light on the screen, surrounded by a dark ring,
followed by other rings alternately bright and dark,
but of rapidly decreasing intensity, till they are lost
in the dark shadow of the screen in which the hole is
pierced. The central bright patch is much larger
than the geometrical projection of the hole.
The continuity of the phenomenon connects the
diffusion of the light which passes through the hole in
the last case, and the comparative absence of diffusion
in the first case, with the formation of coloured fringes
and alternations of intensity about the boundary of
shadows in general, and with the external fringes
belonging to a straight edge in particular, and makes
it probable that if we could explain these last the
principles of the explanation would enable us also to
explain the existence of rays, at least in so far as rays
have a real existence at all.
Can we then explain the external fringes in the
simple case of a straight edge ? Newton made careful
observations of the phenomenon ; but guided as he
was by ideas belonging to the corpuscular theory of
light, he advanced no further towards an explanation
than a few vague conjectures. Dr. Young, guided by
the theory of undulations, was more successful. He
EXPLANATION OF EXTERNAL FRINGES, 6 1
attributed these fringes to the interference of two
portions of light, one coming direct from the luminous
point, and one reflected at a grazing incidence at the
edge of the opaque screen, losing half an undulation
at the reflection. This theory explained very well
the leading features of the fringes, showing them to
be hyperbolic in form, that is to say that a section of
the fringes, conceived as existing in space, made by a
plane passing through the luminous point and perpen-
dicular to the edge, is a system of hyperbolas having
for their common transverse axis the line joining the
luminous point with the edge, and having small con-
jugate axes, differing from one fringe to another of
the system. It explained also the decreasing width
of the fringes as we recede from the shadow, and their
dilatation when the luminous point approaches nearer
to the opaque screen from the edge of which they
start It even gives very nearly the breadths of the
fringes and their distances from the geometrical
shadow.
Accordingly when Fresnel, many years later,
commenced his celebrated researches on diffraction, he
in the first instance adopted Young's theory as to the
cause of the formation of the external fringes. In the
course however of his study he met with phenomena
of diffraction which did not fall in with Young's view,
and which at last opened his eyes to perceive the
62 THE NATURE OF LIGHT.
grand principle which underlies the whole. We have
seen that Huygens successfully explained the laws of
reflection and refraction on the undulatory theory by
introducing the principle that each element of the
front of a wave may be regarded as the source of an
elementary disturbance, and these disturbances must
then be joined together. Now we have only to com-
bine that principle with this other principle, that in
so compounding them we must take due account
of their respective phases, in order to account
for the whole of the phenomena of diffraction,
curious and complicated as they are. In other words,
we have only to combine Huygens's principle with the
principle of interference. These two principles again
are nothing more than special applications of the
general dynamical principle of the superposition of
small motions; a principle which lies at the very
basis of the theory of undulations, and of which the
special applications just mentioned might have been
foreseen.
The application of this principle to special cases,
among others to the case of the external fringes,
involves calculations of considerable complexity.
Fresnel executed these calculations for the external
fringes, and also made a series of most careful and
accurate measurements of the positions of the fringes
referred to the geometrical shadow under a variety of
EXPLANATION OF EXTERNAL FRINGES. 63
circumstances. The theoretical distances of the
several fringes from the geometrical shadow were a
matter of pure prediction ; for the only unknown
quantity involved in the theoretical expression, the
length of a wave, had been determined by Fresnel by
independent methods, some of them, as for example
that depending on the measurement of the fringes
produced by interference mirrors, not involving
diffraction at all, so that not a single arbitrary
constant was left, to be determined by some one
measurement of a fringe in some one particular case,
whereby an at least partial accordance between theory
and observation might have been brought about
On the other hand the distances of the fringes from
the geometrical shadow in a variety of cases were
most carefully measured micrometrically, and the
comparison of the calculated and observed places
manifested a truly wonderful accordance, the average
error being only about the -^^th part of an inch.
The distances calculated from the imperfect theory
of Dr. Young agreed nearly, but not exactly, with
those deduced from the complete theory of Fresnel : in
spite of the smallness of the difference, the measure-
ments were sufficient to discriminate between the two,
and the result was decisively in favour of the complete
theory as given by Fresnel.
As the geometrical shadow is not, like the fringes.
64 THE NATURE OF LIGHT.
a visible object, it may not be superfluous to mention
briefly the mode of referring the places of the fringes
to the geometrical shadow. The fringes were formed
by the cheeks of an aperture with parallel edges, one
of which was moveable by a micrometer screw, by
which means the breadth of the aperture could be
very accurately measured. The cheeks were set a
suflicient distance apart to prevent the fringes formed
by the one affecting in any sensible way those formed
by the other. We thence get from similar triangles,
by the rule of three, the distance apart of the geo«
metrical shadows at the focal plane of the eye-lens.
Now the distance of any particular fringe, say the
first dark fringe, on the right from the same fringe on,
the left can be measured by a micrometer moveable in
the focal plane of the eye-lens. Half the excess of
distance between the geometrical shadows in the
focal plane over this gives the distance of the first
minimum from the geometrical shadow.
The phenomena of diflraction may be varied in-
definitely by varying the outline of the opaque body,
or aperture or apertures pierced in an opaque screen,
as well as the two distances concerned ; and there is a
large class of interesting appearances which may be
seen by using a telescope with which a luminous point
is viewed in focus, and covering the object-glass with
a screen containing one or more aperturesof any fprm
EXPLANATION OF RAYS/ 65
th.^t may be chosen. In this case especially most
curious and beautiful coloured patterns are produced,
so strange and complicated that a person looking at
them for the first time could never guess from the
pattern what was the form of the aperture which
produced it. ;
Besides the case of the internal fringes which was
so carefully examined by Fresnel, a number of other
instances in both classes, that is, without and with a
lens or object-glass combined with the diffracting
body, have been investigated theoretically, and the
results compared with observation. The accordance
is found to be absolutely complete even in the most
minute particulars.
And now at last, as part and parcel of the com-
plete theory of diffraction, we are able to explain the
existence of rays; to show why it is that it is so
nearly true that light proceeds in a straight course
past bodies and through apertures.
The explanation may be given without entering
into mathematical details. Suppose light coming
from a luminous point which for simplicity's sake we
may suppose to be at a practically infinite distance, an
element of the sun's disk for example. Let it fall on
a screen in which is a moderately small aperture, and
consider the disturbance produced beyond the screen
at a point, P, well outside the projectioa of; the
S- 5
66 THE NATURE OF LIGHT.
aperture. Make P the centre of a set of concentric
spheres with radii increasing by half the length of a
wave. These will cut the plane of the aperture in a
series of circular arcs, very close to one another in
consequence of the extreme smallness of the wave
length, and comprising between any two consecutive
circles narrow slips of the aperture, such that two
adjacent slips are very nearly equal in area. Now we
have a right to regard each element of each slip as
the source of an elementary disturbance, which reaches
P after the lapse of a time proportional to its distance
from P, Since corresponding points in consecutive
slips differ by half a wave's length in their distance
from P, and the elementary disturbances from them
accordingly always reach P in opposite phases, so as
to neutralize each other, we easily see that the total
effect of one slip is very nearly indeed neutralized by
that of its neighbour. This is still more nearly true
if we take the disturbance produced by one slip and
the mean of those produced by its two neighbours ;
and in this way, by taking each alternate slip and the
mean of its two neighbours, each slip gets counted
once, and once only, except at the two ends, where,
however, the length of the slips dwindles away to
nothing. Hence there is no sensible disturbance, and
therefore no sensible light, for a point P situated as
we have supposed.
EXPLANATION OF RAYS. 6/
If now we take a point P situated well inside the
projection of the boundary of the aperture, it may be
shown by similar reasoning that the disturbance, and
therefore the illumination, is sensibly the same as if
the screen in which the aperture is pierced were away.
This conclusion rests, it will be seen, on the ex-
treme smallness of the length of a wave, in con-
sequence of which an aperture, unless extremely
small, IS cut a great number of times by a series of
concentric spheres with radii increasing by half a
wave's length. There is no difference of explanation
as regards light and as regards sound, save what de-
pends on the difference of scale entailed by the
difference of wave length. Take as regards light the
case of a small circular hole say the tenth of an inch
in diameter, and of distances from the luminous point
to the screen in which the hole is pierced, and from
that again to the screen on which the light is re-
ceived, of say 8 feet 4 inches, or 100 inches, each. In
this case, regarding the luminous patch on the screen
as a whole, there would be no great diffusion of
light, but the phenomena of diffraction would never-
theless be fairly pronounced. There ought to be a
corresponding case of diffraction for sound ; but on
what scale ? Take 50 inches as the length of a wave
of sound, which would correspond to a musical note
of moderate pitch. Taking as before the t^j^m^
5—2
68 THE NATURE OF LIGHT.
part of an inch as the wave length for light, the
length of the wave of sound will be two and a half
million times as great as the wave length of light
Consequently to obtain the corresponding case of
diffraction for sound, our "small" circular hole would
be obliged to have a diameter of rather more than
4 miles, say 4 miles, and the distances from the source
of sound to the hole through which it passes, and
from that again to the place where the sound is
listened to, would have to be 4000 miles each.
It is remarkable that the existence of rays, which
formed the great stumbling-block in the way of the
early reception of the theory of undulations, is now
shown to belong to a class of phenomena, those of
diffraction, the complete and marvellously simple
explanation of which afforded by the theory of undu-
lations now forms one of the great strongholds of that
theory.
Before leaving this subject I will briefly mention
two or three instances of diffraction which from their
paradoxical character or their importance are de-
serving of notice.
Reverting to the case in which light from a
luminous point passes through a circular aperture, and
is received on a screen beyond, consider the brightness
at a point just in the axis on the receiving screen.
If the relation between the two distances already so
SPECIAL INSTANCES OF DIFFRACTION. 69
often mentioned and the diameter of the hole be such
that the sum of the distances from the luminous point
to the edge of the hole and from thence to the central
point on the receiving screen exceeds the direct
distance from the luminous point to the latter by just
lialf a wave's length, theory shows that the illumina-
tion is actually four times as great as if the screen in
which the hole is pierced were taken away altogether.
Suppose now the hole be enlarged. We might have
said at first sight, supposing we were ignorant of the
theory, *' Of course that must increase the illumination
at the central point, or at any rate cannot diminish
it." On the contrary it Soes diminish it ; and if the
hole be enlarged till its area is just double what it
was in the first instance, the centre of the illuminated
space on the screen is a black spot. This theoretical
result is easily realized in experiment; only as the
wave length varies from colour to colour, and the
proper distance of the receiving screen varies with
the wave length, when the screen is in adjustment for
the brightest part of the spectrum it is not quite in
adjustment for the fainter ends, so that the spot
instead of being perfectly black is faintly purple.
Again, suppose a circular disk is exposed to
radiation from a luminous point, and the shadow is
received on a screen at some distance, or rather
viewed directly through an eye-lens. According to
70 THE NATURE OF LIGHT.
theory, the very centre of the shadow will be a bright
point, as bright as if the disk were away. This
strange result, again, can easily be verified experi-
mentally, easily at least if we are not too ambitious
as to the size of the disk ; for the delicacy of the
experiment increases with the size of the disk, and at
the same time the total quantity of light that we
have to work with decreases. In repeating the ex-
periment I have seen without difficulty the central
spot, with the system of rings round it well formed,
in the centre of the shadow of a disk of about the
gize of a sovereign.
Among the class of diffi-action phenomena in
which a luminous point or line is viewed in focus
through a telescope, and a screen with one or more
apertures is placed in front of the object-glass, there
is one case of very special interest. It is that in
which a line of light is used, suppose an extremely
narrow slit through which the sun's light is reflected
horizontally, and a fine carefully ruled grating is
placed opposite to the object-glass, the lines of the
grating being parallel to the slit The best results
are obtained with gratings consisting of glass, or
sometimes metal, on which fine parallel lines are
ruled with a diamond point It is requisite that the
lines should be very accurately equidistant, and in
fine gratings they are so close that several thousand
SPECTRA WITH A GRATING. 7 1
go to an inch. If the grating thus constructed be
of metal, it can only of course be used for reflec-
tion.
Now on viewing through the telescope the light
transmitted through or reflected from such a grating,
a most remarkable appearance is presented. The
luminous line is seen through or by reflection from
the grating as if the ruled lines were away, and right
and left of it for some way the field is dark. But
then on both sides we gttpure spectra, the blue ends
being nearest to the axis. These are followed by a
second set of spectra, the blue ends of which overlap
the red ends of the former, and so on, the spectra as
we proceed overlapping one another more and more.
So pure are these spectra if the grating be a good one,
that they show the fixed lines of Fraunhofer to per-
fection.
The formation of these pure spectra can easily be
explained, and the formula expressing the deviation
for light of any one kind in the spectrum of any
order in terms of the interval of the grating, the
angle of incidence, and the wave length for that kind
of light obtained, from the general principles of the
theory of undulations. But by mounting the grating
in the axis of a horizontal graduated circle which
carries the telescope, the deviations can be measured
with extreme precision. The interval of the grating
7? .'THE NATURE OF LIGHT.
is got by measuring the breadth of the ruled space,
and dividing by the number of ruled lines less one.
We thus have the means of determining the wave
lengths, if the theory be true, for as many definite
Jcinds of light marked by definite lines as we please;
and by comparing the wave lengths measured by
means of spectra of different orders, at different
inclinations of the incident light to the grating, and
by different gratings, we have a very sharp test of the
truth of the formula deduced from theory. The
accordance is complete; and that being so we are
justified in the interpretation assigned to that measur-
able quantity which . we^qall a wave's length, and
obtain its value witfe'gl^^^recision.
I may here perh^p?-mention that it has even been
proposed to take the length of a wave of light of some
particular kind, such for example as that belonging to
one component of the double yellow line of a soda
flame, as a natural standard to which a national
standard of length might be referred in case of loss.
The French refer their metre to the dimensions of
the earth. The English refer their yard to the
length of the seconds' pendulum. But supposing
the earth to be slowly contracting by cooling, both
these natural standards would be liable to be affected
in the course of ages ; and if such a catastrophe were
to occur as the impact on the earth of some great
ACCURATE MEASUREMENT OF WAVE LENGTH. /$
globe visiting our solar system, the dimensions of the
earth and the value of gravity, and accordingly the
length of the seconds' pendulum, would at once be
affected to an unknown degree. But the wave length
of light of a given kind would remain unchanged,
and the survivors of such a catastrophe might have
recourse to it to recover the ancient standard of
length.
PnifP"
LECTURE III.
Closer examination of the fundamental suppositiofis of the
Theory of Undulations — Survey of the conclusions ar-
rived at by a study of the phenomena of common light —
Elementary facts of double refraction and polarization.
It has been my aim in these lectures to endeavour
to give you some definite idea of the evidence on the
strength of which we assert that light consists in un-
dulations propagated in a medium filling the inter-
stellar spaces. To enable you to judge more fairly of
the evidence, I have attempted to present the subject
in an inductive rather than in a deductive form. Instead
of starting with a number of hypotheses, originating
you would not know how, and then showing how the
conclusions following from them are in accordance with
observed results, I have commenced with only the
most fundamental conceptions of undulations, and of
the conditions which we must suppose to obtain in
order that they may exist, and have afterwards supple-
mented our original rather crude conceptions in the
manner which a study of the phenomena showed to
CLOSER EXAMINATION OF HYPOTHESES. 75
be necessary. We have seen that not merely are the
laws of reflection and refraction in agreement with
the theory, but the curious and complicated phe-
nomena of interference and diflraction are explained
by it to the minutest particular. What strikes one
most about the theory is what has been truly de-
scribed as its astounding simplicity. This so carries
on the face of it the stamp of truth, that to one who
is familiar with the phenomena as well as the theory,
an overwhelming conviction is produced that it is
indeed true to nature. That being the case, it may
be well now to examine the various hypotheses
which must be made in some greater detail than
has hitherto been done.
The fundamental hypothesis of the existence of a
medium to which we give the name of ether, I have
already mentioned. To account for undulations in this
medium, we must attach to it the two radical con-
ceptions of inertia and elasticity. First, a finite time
must be required in order to generate in a finite
portion of it a finite velocity by the action of a finite
force. Secondly, a change of condition of some kind
in the ether consequent on a relative displacement of
its parts must call into play a force of restitution
tending to restore it to its primitive condition. Thus
in air condensations and rarefactions produce re-
spectively an increase and a diminution of pressure.
76 THE NATURE OF LIGHT.
SO that any small portion of the air which has been
contracted or expanded tends to push out the sur-
rounding parts, or to be compressed by them, and so
to return to its primitive state ; and it is to the forces
of restitution thus called into play that the propaga-
tion of sound is due. Naturally therefore those who
adopted the undulatory theory of light were led to
imagine the ether as possessing a similar kind of
elasticity. There is however a whole class of phe-
nomena which I have not yet so much as named, and
which have no counterpart in sound, the study of
which has led us to conclude that the elasticity of
the ether is of an altogether different nature from
that of air. The question of the relation between the
direction of vibration of the particles of ether and the
direction of propagation of the light is bound up
with that of the character of the elasticity by virtue
of which the undulations are propagated. In the
explanation, however, of the ordinary phenomena of
interference and diffraction, we are not concerned
with the direction of vibration; in interference for
instance, where we always have two streams of light
from the same source pursuing nearly the same paths,
and coming together either in the same direction, or
in directions very slightly inclined to each other,
whatever be the direction of vibration in one of. the
interfering streams, the same, or very nearly indeed
CLOSER EXAMINATION OF HYPOTHESES. 7/
the same, will be the direction in the other, and that
IS all that we are concerned with in the explanation.
And the explanation of the ordinary phenomena of
diffraction has, as we have seen, been resolved into
the interference, not of two, but of an infinite number
of infinitely small disturbances all coming originally
from the same source, and following very nearly the
same paths.
The mode of excitement of the undulations in the
first instance is in some respects analogous to the
mode of excitement of sound by a vibrating body,
such as a bell, but in some respects distinctly different.
A bell in exciting vibrations in the surrounding air
acts as a continuous elastic body ; in explaining the
mechanical action, we have nothing to do with
speculations as to the molecular constitution of
ponderable matter. But the fact that the spectra of
flames show bright lines depending on the nature of
the chemical substances in the flame, shows that in
the excitement of the ethereal vibrations we have in
many cases, if not in all, to do with the vibrations of
the constituent parts of the chemical molecules of
which we have reason to believe that ponderable
matter consists.
The explanation of refraction on the theory of
undulations requires us to suppose that in refracting
media, such as glass or water, the vibrations are
78 THE NATURE OF LIGHT.
propagated more slowly than in what we call vacuum.
In fact, theory shows that the sine of the angle of
incidence must be to the sine of the angle of refrac-
tion in the ratio of the velocity of propagation in
vacuo to the velocity of propagation in the medium.
The question then arises, When light passes through
water or air, what is the vibrating medium ?
At first sight we might say, of course the water or
the glass itself. But this supposition will not bear
examination. We know too much of the elasticity of
water and glass to allow us to explain the result in
that way. Water is sometimes spoken of as incom-
pressible, but we know that it yields slightly to a
compressive force. The amount of compressibility
can be measured by hydrostatic means, and from
thence the velocity of propagation of sound in water
can be determined by calculation. It comes out
about four times as gpreat as that of sound in air,
which agrees very well with the experimental measure-
ment of the velocity which has been made in the Lake
of Geneva.
Glass, and isotropic elastic solids in general,
possess two distinct kinds of elasticity, one, by which
they resist compression of volume, the other, by
which they resist a distortion not involving alteration
of volume, but opposed by the force by which the
substance resists the gliding of one part over another,
CLOSER EXAMINATION OF HYPOTHESES. 79
a gliding which takes place freely in liquids. The
two elastic constants of glass have been carefully
determined, and from them can be calculated the two
velocities of propagation of two kinds of disturbance
which a large mass of glass would be capable of
transmitting. These come out greater no doubt than,
but still comparable with, the velocity of propagation
of sound in air, and are therefore almost immeasurably
smaller than the velocity required to account for the
refraction of light on the supposition that it is the
glass itself that vibrates. In fact, the velocity of
light in vacuum is nearly 1,000,000 times as great as
that of sound in air, and the velocity of light in
glass would be equal to its velocity in air divided by
the index of refraction of glass, or say about 600,000
times that of sound in air, so that it is altogether of a
different order of magnitude.
Again, consider a gas or mixture of gases, such as
air, in its relation to Light. Air can be rarefied till
we have a near approach to an interstellar vacuum, or
again can be condensed till its density becomes
comparable with that of a liquid. Yet all through
these changes there is a perfectly continuous change
in its relations to light It will not do therefore to
say that light is propagated through air in one way,
by one sort of mechanism, when the air is very rare,
and by another when the air is very dense. But
80 THE NATURE OF LIGHT.
when air is rare, and makes a near approach to what
we call vacuum, but which we must now conceive as
space filled with the luminiferous ether, it is clear that
it must be by the vibration of the ether that light is
propagated in it. We are led therefore to conclude,
from these considerations again, that when light is
propagated in a gas condensed till its density becomes
comparable with that of a liquid, and accordingly
in liquids also, and in solids like glass, which
behave with respect to light just as liquids, it is
ether existing in the interstices between the molecules
of the bodies, of which the vibrations constitute the
light that passes through them.
We might not perhaps have been disposed in the
first instance to suppose that such a solid material
as glass really had ether pervading it. But we must
beware of applying to the mysterious ether the gross
notions which we get from the study of ponderable
matter. The ether is a substance, if substance it may
be called, respecting the very existence of which our
senses give us no direct information ; it is only
through the intellect, by studying the phenomena
which nature presents to us, and finding with what
admirable simplicity those of light are explained by
the supposition of the existence of an ether, that we
become convinced that there is such a thing. We
know that a magnet attracts iron through a piece of
CLOSER EXAMINATION OF HYPOTHESES. 8 1
glass ; and yet the magnetic influence is one which we
can neither see nor feel : why then should not ether
exist within glass, and be capable of vibrating within it?
It may readily be imagined, as more probable
than the contrary, that the presence of the ponderable
molecules interspersed through the ether, within the
region of space which is enclosed by the surface of
the glass, may have the effect of altering the velocity
of propagation of the ethereal vibrations within it, and
very probably diminish it. But what may be the
precise mechanism by which this result is brought about
we do not know. It is easy to frame plausible hypothe-
ses which would account for the result, but it is quite
another matter to establish a theory which will admit
of, and which will sustain, cross-questioning in such a
variety of ways that we become convinced of its truth.
It follows from Huygens's explanation of the law of
refraction, which assumes nothing but what lies at the
very foundation of the theory of undulations, that the
ratio of the velocity of propagation of light in vacuo
to its velocity in a medium, such as glass or water,
must be equal to the index of refraction, and must
therefore vary from one colour to another, increasing
from the red to the violet, sometimes, as in the case of
oil of cassia, as much as 6 per cent, and upwards
within the limits of the visible spectrum. Now we
know that in sound notes of different pitch are propa-
S. 6
82 THE NATURE OF UGHT.
gated with the same velocity, as also follows from
theory, and it has been suggested that it is a difficulty
in the way of the theory of undulations that the case
must be so different with light I cannot say that it
appears as such to my own mind ; for the case of the
vibration of one of two mutually penetrating media, as
for example glass and the ether, is so different from
any that we have to deal with in the case of sound
that we cannot argue from the one phenomenon to the
other. If indeed it were established that the velocity
of light in a vacuum differs from one colour to another,
we should then have to allow that an analogy which
might have been expected to hold good between the
two phenomena does not really do so. But till very
lately the observed phenomena which reveal a finite
velocity of light, and the experiments which had been
made to determine the velocity directly, all yielded a
negative result as to any difference of velocity between
one colour and another, so that the difference in the
ratio above-mentioned was attributable to a difference
of velocity in the refracting medium. I have said
'* till lately," because in a paper by the late Dr James
Young and Professor George Forbes, presented to the
Royal Society between two and three years ago, and
printed in the PhilQSophical Transactions, in which
the authors have determined experimentally the ve-
locity of light by a method founded on that of Fizeau,
CLOSER EXAMINATION OF HYPOTHESES. 83
but presenting certain new features, it is mentioned as
a result of the observations that blue light seemed to
travel faster in air than red light. The method
employed is founded on the judgment of the observer
as to the equality of intensity of two points of light, or
artificial stars, seen simultaneously in the field of view.
It is difficult to see any possible source of instrumental
error which could have led to the above conclusion as
to a variation of velocity depending on the colour ; on
the other hand, the conclusion rests on the judgment
of the eye of a single observer ; and till the question
has been further tested it would seem to be premature
to regard the difference as established. Should it be
confirmed by further observation, it will then be
necessary to consider whether the circumstance that
the light was propagated in a field of magnetic force,
namely the earth's magnetic force, may have had some-
thing to do with it However even if the result of
further enquiry should be to show that the different
colours are propagated at different rates in a simple
vacuum free from disturbing influences, all we should
be entitled to say is that the expectation which we were
led to form beforehand from the analogy of sound,
and from the supposition that the forces whereby one
portion of ether acts directly on another are insensible
at finite distances, at distances even comparable with
^^ goioo ^^ P^^ of an inch, has not been verified.
6 — 2
84 THE NATURE OF LIGHT.
As r^ards the mode of perception, while there
are analogies between sound and light there are at
the same time notable differences. In sound, the tym-
panum of the ear is thrown mechanically into vibration,
and the nerves of hearing are mechanically affected, as
^ mechanical disturbance of a point on the surface of
the body is made known by the sense of touch. But
in light, just as we have seen reason to believe that it
is the disturbance of the ultimate molecules, or of their
constituent parts, by which the vibratory motion which
constitutes light is in the first instance communicated
from ponderable matter to the ether, so we have reason
to think that when light is absorbed what takes place is
that the disturbance of the ether is communicated, not
to portions of matter regarded as forming portions of a
continuous elastic body, but to the ultimate molecules
of which matter consists, or to their constituent parts.
It may be that temporary chemical changes are
thereby produced in the ultimate filaments of the
nerves of the retina, in which case the sense of sight
would be more analogous to the sense of taste than to
that of touch.
Corresponding theoretically to this difference is
the fact that in light we have absolutely nothing
answering to the sensation of harmony in sound.
When two musical notes have their times of vibration
in some simple ratio, we have concord when they arej
/
STRIKING CHARACTER OF CONCLUSIONS. 8S
sounded together; thus the ratio of 2 to 3 gives
a fifth, that of 4 to 5 a major third &c, whereas
when two notes sounded together have their times of
vibration in no simple ratio, we have discord. But
when two kinds of light, each of definite refrangibility,
and accordingly of definite periodic time, are mixed
together, there is no pleasing or disagreeable sensation
depending on whether the periodic times are in some
simple proportion or not
And now before passing on to a totally different
branch of the subject, the study of which leads us to
believe that the properties of this mysterious ether
must be veiy different from what we should have
imagined beforehand. It may be well to pause and
contemplate for a little the wonders with which our
study of the phenomena up to the present point has
shown that we are surrounded.
First, we learn to regard the interplanetary and
interstellar spaces as no mere vbid, or empty space
passed through by swift . messengers in the shape of
particles of light conveying information from distant
worlds, but as filled with an ever present, all pervading
substance, in which the ultimate particles of ponderable
matter, including those of our own bodies, are con-
tinually as it were bathed, and yet of which our senses
give us no direct cognizance.
Secondly, that whatever other important offices
86 THE NATURE OF LIGHT.
this ether may fulfil, this one at any rate belongs to it,
that it forms the medium of visual communication
between ourselves and our fellow creatures, between
ourselves and the various objects around us, between
ourselves and distant worlds.
Thirdly, that this communication is carried on by
tremors of some kind propagated through the ether
with a* velocity so enormous that for all practical
purposes of communication on earth it may be deemed
instantaneous. In fact, light would travel about
seven and a half times round the whole earth in one
second. But so Jrapid are these tremors that many
hundredsof miUiortsof millionstake place in one second.
"Notwithstanding therefore the enormous rate of prd-
pagation^ the lengths of the waves are excessively
small, ranging about the ^^j^th part of an inch.
It has been shown that it is this excessive small-
ness of wave length which enables light to be propa-
gated so nearly in a straight course, in independent
rays. Were it not for this, the formation of sharp
images would be impossible. Were the lengths of
the waves of light comparable with the lengths of the
waves of sound, we should as regards the use of our
eyes be nearly in the condition of a man who was all
but blind; who could just distinguish light from
darkness, or a gleam of red from a gleam of green,
and no more. We should be in this condition if the
STRIKING CHARACTER Of CONCLUSIONS. 87
time of a vibration were anything like so great as the
one hundi^ millionth part of a second, in which case
the length of a wave of light would be comparable
with that of a wave of sound.
Fourthly, we learn that notwithstanding the
almost inconceivable shortness of the time of vibra-
tion^ a variation in this periodic time is nevertheless
recognisable by our senses, and that it is to this cause
it is due that the face of nature does not present
to us simply light and shade, like a photograph, but
that we have tliat endless variety of colour which we
enjoy.
Fifthly, in the plan of an elastic medium con-
veying small vibrations, we have a mechanism of the
simplest possible kind having for result that rays of
light from objects all around cross each other*s paths
in all sorts of ways without any mutual disturbance.
When we survey a varied landscape, each visible
point in it,however minute, may be regarded as an inde-
pendent source of light, from which the light proceeds
in all directions. True, the objects are not in general
self-luminous ; they are seen by the light of the sun or
of the clouds which they irregularly reflect, but as
regards the behaviour of the pencils which proceed
from them they are as good as self-luminous. Well
then ; from each visible point, however minute, there
enters the eye every sqcond a length of light of
88 THE NATURE OF LIGHT.
about i86/xx> imle% that is, h^t wliidi would have
travelled tbat distance had not the eye been diere to
catdi it, this immense length beii^ filled with undu-
lations of lengths langii^ about 50/XX) to the inch.
And if die landscape be contemplated by a multitude
of persons, from each visible point in it that vast
length of light, ccHisisting of undulations of such
excessive minuteness, enters the eye of each spec-
tator every second of time; and all these various
streams of light, proceeding in all sorts of directions,
cross each odier's paths in all sorts of ways without
the slightest mutual disturbance.
To one previously unacquainted with the subject,
these statements seem like the dreams of an enthu-
siast, or at best the speculations of some wild theorist,
and yet there is nothing in what I have stated
beyond the sober conclusions of scientific invest^-
tion, conclusions supported by an amount of evidence
altogether overwhelming. In saying this it is to be
remembered that the precise mode of disturbance of
the ether has been left an open question.
In studying this subject, one can hardly fail to be
struck with the combination of these two things : —
the importance of the ends, the simplicity of the
means. When I say the importance of die ends, I
use a form of expression which is commonly emplojred
as expressing des^. And yet on that very account
EVIDENCE OF DESIGN. 89
we must be on our guard against too harrow a view.
When we consider the subject of vision in its entirety,
the construction of the recipient organ as well as the
properties of the external agent which affects it, the
evidence of design is such, it seems to me, as must
to most minds be irresistible. Yet if I may judge of
other men's minds by my own, it is rather in the
construction of the recipient organ than in the prO'
perties of the agent that affects it, that the evidence
of design is so strongly perceived. And the reason
of this may be that we are here dealing with what
more nearly resembles design as we know it in our-
selves. Man takes the laws of matter as he finds
them; the laws of cohesion, of the conversion of
liquid into vapour, of the elasticity of gases and
vapours, and so forth ; and in subserviency to those
laws he constructs a machine, a steam-engine for
instance, or whatever it may be ; but over the laws
themselves he has absolutely no control. Now when
we contemplate the structure of the eye, we think of
it as an organ performing its functions in subserviency
to laws definitely laid down, relating to the agent
that acts upon it, laws which are not to be interfered
with. We can it is true go but a little way towards
explaining how it is that through the intervention of
the eye the external agent acts upon the mind. Stilly
there are same steps of the process which W0 are able
..'^'
90 THE NATURE OF LIGHT.
to follow, and these are sufficient to impress us
strongly with the idea of design. The eye is a highly-
specialized organ, admirably adapted for the important
function which it fulfils, but, so far as we can see, of no
other use ; and this very specialization tends to make
the evidence of design simpler and more appareot.
But when we come to the properties of the external
agent which affects the eye, we begin to get out of
our depth* These more nearly resemble those ulti-
mate iairs of matter over which man has ho control ;
and to say that they were designed for certain
important objects which we perceive to be accom-
plished in subserviency to them, seems to savour of
presumption* It is but a limited insight that we can
get into the system of nature ; and to take the very
case of the luminiferous ether, while as its name
implies it is all important as regards vision, the present
state of science enables us to say that it serves for
one object of still more vital importance ; we seem to
touch upon another ; and there may be others again
of which we have no idea.
In the study of those phenomena of light which I
have hitherto brought before you, we derived .con-
stant assistance from our knowledge of the theory of
$ound. . I now come to a branch of the subject where
the theory of sound fails us altogether, to a class of
DOUBLE REFRACTION. ^t
optical phenomena which have nothing answering to
them in sound. I refer to double refraction and po-
larization.
Of these phenomena, the former of which is so
closely related to the latter, double refraction was the
first to be discovered. It was in 1669 that Bartho-
linus published his account of the discovery of a
strange and unusual refraction in Iceland spar. The
subject was taken up and investigated with the keen-
est interest by Huygens, whom we must regard as the
founder of the theory of undulations. It would not
be in accordance with the object which I have had in
view in these lectures to enter into details respecting
the phenomenon, and I must content myself with
mentioning a few of the more salient features.
Iceland spar stands we may say alone among
minerals in at the same time possessing powerful
double refraction and occurring in large clear crys-
talline masses. It was this circumstance which led
to the discovery. The mineral cleaves very readily
in three definite directions, so that a block obtained
by cleavage is of the form of a parallelepiped. The
three obtuse dihedral angles of this parallelepiped are
all exactly equal, and are so turned that two opposite
solid angles are contained by three equal obtuse
plane angles, while each of the remaining six is
contained by one obtuse and two acute. A direction
g2 THE NATURE OF LIGHT.
— not, observe, any special line — equally inclined to
the three edges which meet in one of the obtuse solid
angles is called the axis of the crystal. The crystal-
line structure, so far at least as it is revealed by the
cleavage planes, or I may add by the natural faces, is
symmetrical with respect to three planes and no
more, each of these being parallel to one of the edges
which meet in an obtuse solid angle, and perpendicu-
lar to the plane of the other two, and accordingly
being parallel to the axis of the crystal. Any one
of these planes is what Huygens called a principal
plane.
If an object near at hand be viewed through such
a block, as for example if the block be laid on a
printed page, two images of the object are seen, of
which one appears more elevated than the other when
both eyes are used, indicating a stronger refraction.
This image is called the ordinary, because it obeys
the ordinary law of refraction. That such is the
case was found by Bartholinus, and confirmed by
Huygens ; and the accuracy of the ordinary law as
applicable to this pencil had stood the test of the
most refined measurements carried out by the most
improved modern methods, among which I may
specially mention the measurements made by Pro-
fessor Swan and Mr Glazebrook. But the rays
belonging to the other or extraordinary y as it is called,
• DOUBLE REFRACTION. 93
image must obey some totally different law. If the
eye and object be in the principal plane of the block,
the extraordinary ray obeys the laws of ordinary
refraction so far as this, that the refracted ray lies
in the plane of incidence ; but whereas in ordinary
media there is no refraction at a perpendicular inci-
dence, and at oblique incidences there is refraction,
which goes on increasing as the angle of incidence
increases, in the case we are now considering there
is refraction at a perpendicular incidence, and at one
particular oblique incidence a ray passes through
without refraction. And if the block be turned round
in the plane of its surface, so that the plane through
the eye and the object, which I suppose perpendicu-
lar to the plane of the surface, is no longer a principal
plane of the crystal, the refracted extraordinary ray
does not so much as lie in the plane of incidence.
If a distant object be viewed through the block,
there is no duplication, so that whether a ray passes
through the block as ordinary or as extraordinary,
the emergent ray to which it gives rise is parallel to
the incident, just as in the case of ordinary refraction.
This is true whatever be the inclination of the inci-
dent ray to the surface, and whatever be the plane of
incidence. It depends however on the parallelism of
the surfaces of incidence and emergence ; and if these
surfaces be inclined to each other, forming a prism,
94 THE NATURE OF LIGHT.
then the duplication of a distant object is at once
perceived. If a slit of light be viewed through such
a prism, two spectra are seen, which are unequally-
deviated, and show in general unequal dispersion.
Now what notion are we to form of the cause of
double refraction if we adopt the theory of undula-
tions? According to the fundamental explanation
of refraction given by Huygens, as there are two
refracted rays, there must be two disturbances pro-
pagated within the crystal as the result of an elemen-
tary disturbance excited at a point of its surface, and
these two must travel with different velocities. They
will spread out from the centre of disturbance in two
closed surfaces respectively, or it may be a surface
with two sheets. For one of these, the velocity of
propagation will be the same in all directions, and the
surface will therefore be a sphere. This follows from
the fact that the ordinary ray obeys the ordinary law
of refraction. But as the other obeys some' more
complicated law, the surface for it must be other than
a sphere, and the velocity of propagation must be
different in different directions.
It has been already remarked that there are three
planes of crystalline symmetry, and these, as might
have been expected from the intimate relation of the
optical properties to the crystalline structure, . are
also planes of optical symmetry ; that is to say, all the
DOUBLE REFRACTION. 95
optical properties are symmetrical with respect to
each of them. But there are other planes which are
planes of optical, though not of crystalline, symmetry.
Thus if a plate be cut perpendicular to the axis, the
optical properties in. it are symmetrical with respect
to any plane through the axis ; and if a plate be cut
parallel to the axis, the plane perpendicular to the
axis is a plane of optical symmetry as well as the
plane passing through the axis, though the former
cannot be, and the second is not in general, a plane
of crystalline symmetry. In short, all the optical
properties are symmetrical about the axis, the two
poles of which are alike, so that the optical- properties
present the same degree of symmetry as an ellipsoid
of revolution*. Accordingly the wave surface re-
lating to the extraordinary ray must have thus much
symmetry; and Huygens assumed for trial that it
was a spheroid of revolution. As far as he could
make out, the refraction in the direction of the axis
appeared to be the same for the two rays, and he
accordingly supposed that the sphere belonging to
the ordinary ray, and the spheroid which he assumed
* AccordiDg to Sir David Brewster, this is not altogether the case
so far as relates to the properties of the light reflected from an artificial
sur&ce of the crystal. His observations appear never to have been
published in detail, nor has anyone else, so far as I know, taken up the
subject.
96 THE NATURE OF LIGHT.
as the form for the extraordinary, touched one
another in the axis. This equality of refraction
along the axis we now know to be rigorously exact.
The form of the wave surface being assumed, the
refraction of the extraordinary ray followed at once
from Huygens's construction ; and the mode and
amount of refraction were found to agree with the
construction as near as the most accurate measure-
ments made by Huygens could decide. Mr Glaze-
brook has recently executed a series of measurements
of the refraction of the extraordinary ray in Iceland
spar with all the exactitude of modern methods,
guided by our increased knowledge of the subject;
and the result is that no certain error of Huygens's
construction can be detected.
So far however the laws of the extraordinary
refraction in Iceland spar are merely empirical, based
upon a happy guess as to the form of the extra-
ordinary wave surface; it remains to be explained,
if explain it we can, why there should be these two
kinds of disturbance at all within the crystal, and why
the form of the wave surface should be what we find
it must be if the most fundamental principles of the
wave theory are true, by which the form of the
surface is connected with the observed refraction.
Huygens imagined that the ordinarj'* ray was pro-
pagated by the vibration of the ether within the
POLARIZATION. 97
crystal, while in the extraordinary the molecules of
the crystal took part as well as the ether. I have
already mentioned some of the strong objections
which exist to the supposition that the propagation
of light in media such as water or glass takes place
by vibrations of the ponderable matter ; and similar
objections in good measure apply to the supposition
that both the molecules and the ether take part in it.
But be that as if may, Huygens himself, when he had
nearly concluded his researches, discovered a remark-
able phenomenon which ill accords with the supposi-
tion of his which I have just mentioned.
Suppose a second block of Iceland spar to be
placed on top of the first, so that the two are in the
same relative position which they would occupy if
they formed one larger block. Then neither of the
images, ordinary or extraordinary, seen through the
first block is split into two in passing through the
second block, but the ordinary of the first furnishes an
ordinary in the second, and nothing more, and simi-
larly the extraordinary an extraordinary. The same
is still the case if the second block be separated from
the first, or even inclined by turning in the principal
plane. But reverting for simplicity's sake to the first
relative position of the blocks, suppose that the second
is turned round the common normal to the two
adjacent surfaces. The moment the second block is
S. 7
98 THE NATURE OF LIGHT.
turned from the primitive position, each of the iniages
which the first block furnishes is split into two by
the second block. The relative positions of the two
images forming the pair into which either of the
original images is split is just the same as if that
original image had been formed by common light,
but the intensities are different. When the second
block has been turned through only a small angle,
the ordinary of the first furnishes mainly an ordinary
in the second, but also a faint extraordinary, and
similarly the extraordinary of the first furnishes main-
ly an extraordinary in the second, but also a faint
ordinary. As the turning goes on, the faint images
get brighter, and the bright images get weaker, till
after turning through 45® the four are alike. As the
rotation continues, the pair of images that had been
the weaker get the brighter, and the pair that had
been the brighter get the fainter, till after turning
through 90® the pair of images that had at first
appropriated the whole of the light disappear alto-
gether, and the pair that began to spring into exis-
tence on first turning now alone are seen. In this
position, that is to say when the principal planes of
the two blocks are perpendicular to each other, the
image formed by light which suffered ordinary refrac-
tion in the first block furnishes nothing but an extra-
ordinary in the second, and the image formed by
POLARIZATION. . 99
light which suffered extraordinary refraction in the
first furnishes nothing but an ordinary in the second.
As the rotation goes on, the same series of changes
are repeated, so that in a complete revolution the two
pairs of images vanish alternately at every quarter of
a revolution.
On account of the fundamental importance of this
phenomenon, I must crave your indulgence for dwelling
on it at some length, even though from its elementary
character it must be faniiliar to those of you who have
paid any attention to this branch of the subject
Suppose that light coming directly from a lumi-
nous source, such as the flame of a lamp, is received
on a screen with a circular hole. The screen will
isolate a beam of light which, as I shall have
occasion to deal with it only at short distances
from the hole, I will call cylindrical. Let this beam
be received, suppose perpendicularly, upon a block
of Iceland spar bounded as usual by cleavage planes.
In passing through the spar, it will be divided into
two, an ordinary beatn, which will pass straight on,
and an extraordinary which will be deviated in a
lateral direction in passing through the block, and
will give rise to an emergent beam parallel to the
incident, and accordingly parallel to the first emergent
beam. If the hole in the screen be not too large to.
suit the thickness of the block, the two beams will
7—2
100 THE NATURE OF LIGHT.
come but without overlapping, and may be examined
apart. They are found to be of sensibly equal in-
tensity whatever be the azimuth of the block around
its normal. Making abstraction of the small quantity
of light which goes elsewhere by reflection, we may
say that the whole of the incident light is divided
equally between the two beams.
Suppose now that we fix the block in any position,
say with its principal plane vertical, and place a second
screen with a circular hole to let pass the beam which
went straight through the first block, while it stops the
other. On examining this beam by a second block,
which is turned round, we find that it is divided into
two of unequal intensity, which vanish alternately at
every quarter of a revolution, the whole of the light
passing into an ordinary beam in the second rhomb
when its principal plane is vertical, and into an
extraordinary when it is horizontal. Hence whereas
a beam of common light is propagated in some
definite direction, but possesses no relation to space
in any other direction, so that there is no plane
passing through it which we can distinguish, merely
by the properties of the beam itself, from any other,
the beam we are now considering, namely that which
passed through the second screen, possesses properties
with respect to directions in space transverse to its
direction of propagation ; and if we knew nothing of
POLARIZATION. lOl
Its history, but it were merely presented to us for
examination, that would not hinder us from recog-
nising, by means suppose of a rhomb of Iceland spar,
the peculiar properties which it possesses, nor from
fixing by observation alone the direction of those two
rectangular planes, vertical and horizontal in the case
supposed, with respect to which its properties are
symmetrical, and in either of which if the principal
plane of the examining rhomb be placed, an ordinary
or an extraordinary beam, as the case may be, is
alone produced in it. Light possessing this property,
however it may have acquired it, is said to be polarized,
and the plane with respect to which its properties are
the same as are those of the ordinary ray in Iceland
spar with respect to the principal plane, is called the
plane of polarization. Its azimuth may be determined
experimentally as being that of the principal plane of
an examining rhomb when so turned as to transmit
only an ordinary beam.
To go back now to the first arrangement, namely,
that of a beam isolated by a first screen falling on a
rhomb of Iceland spar, and then on a second screfert
provided like the first with a suitable hole, let this
second screen be so placed as to transmit the beam
which passed through the rhomb by extraordinarj' re-
fraction, and stop the other, and then let the beam be
presented for. observation. On examining it witfi a
i02 THE J^ATURE OP LIGHT.
second rhomb we should find that it possessed iden-
tically the same properties as the beam obtained by-
ordinary refraction in the first rhomb, save that the pro-
perties of this beam are related to the horizontal plane
precisely as were those of the former beam to the verti-
cal plane ; and it is into the horizontal plane that the
principal plane of the examining rhomb must be turned
in order that nothing but an ordinary beam may be
transmitted through it. Hence, according to our
former definition, we must say that the extraordinary
beam passing through Iceland spar is polarized in a
plane perpendicular to the plane of incidence.
More than a century elapsed after Huygens's
discovery of what we now call polarization before
it was known that polarized Light could be obtained
otherwise than by or as an accoippaniment of double
refraction^ But in 1808 Malus made the very impor-
tant discovery that when Light is reflected from glass
at a certain angle, the reflected ray is wholly polarized ;
and since the properties of the reflected ray are the
same with reference to the plane of incidence as are
those of the ordinary ray in Iceland spar with reference
to the principal plane of the crystal, we must in
accordance with our definition say that the reflected
light is polarized in the plane of incidence. The
light reflected at other inclinations possesses all the
properties of a mixture of common light with light
POLARIZING ANGLE. 103
polarized in the plane of incidence, and may accord-
ingly be said to be partially polarized in the plane of
incidence. The transmitted light, whether the light
be incident at the polarizing angle or the angle of
incidence be arbitrary, is found to be partially po-
larized in a plane perpendicular to the plane of
incidence.
Malus found that Light is thus polarized by
reflection from transparent substances in general,
from varnishes &c., but not from metals, the light
reflected from which is found to be only partially
polarized in the plane of incidence. The angle of
incidence on transparent substances required for com-
plete polarization Malus found to vary from one to
another, though he did not discover according to
what law, a law afterwards made out by Brewster,
namely, that the polarizing angle is that for which
the reflected and refracted rays are perpendicular to
each other ; or, as it may be otherwise expressed, the
tangent of the polarizing angle is equal to the index
of refraction.
Malus's important discovery of the polarization of
Light by reflection proves that polarization, whatever
it may be, is something that may exist altogether
independently of double refraction, and must therefore
be something intimately bound up with the nature of
Light in itself. The intimate connexion of double
ICP4
THE NATURE OF LIGHT.
refraction with polarization shows that we cannot
hope to explain the former of these phenomena
unless we can obtain some insight into the nature of
what constitutes polarization.
LECTURE IV.
Phenomena presented on interposing a crystalline block or thin
plate in the path of Polarized Light which is subsequently
analyzed — Laws of Interference of Polarized Light —
IVieory of Transverse Vibrations — Conclusion,
We have seen that when a beam of polarized light
is examined by a rhomb of Iceland spar, it is divided
into two of in general uhe'qual intensity passing
through the spar. As before^-^ttke abstraction of the
snlall quantity of light which goes elsewhere by
reflection, and call the intensity of the incident beam
unity, and let us consider in the first instance the
intensity of the beam which passes through the
examining spar as ordinary. Let A be the azimuth
of the principal plane of the examining rhomb referred
to the plane of primitive polarization. Then the in-
tensity, the relation of which to the angle A is the
object of our search, must be such that it is equal to
unity when A is nothing, decreases to nothing as A
increases to 90^ increases to unity again as A increased
to I8o^ decreases again to nothing as A increases to
I06 THE NATURE OF LIGHT.
270^ and finally increases to unity as at first as A
increases to 360®, having furthermore the same value
for A negative as for A positive, and for go^^A
negative as for 90° — -4 positive. A very simple
function possessing this property is cos^A. If this
be the intensity of the ordinary, since the rest of the
light passes into the extraordinary, the intensity of
the latter must be i — cos' A, or sin' A, or the squared
cosine of the angle between its plane of polarization
and the plane of primitive polarization. Such was
the law assumed by Malus, and called after his name.
It has been verified by photometric measurements,
and is of great importance with reference to the
theory of what it is which constitutes polarization.
Suppose that light polarized in any way is subse-
quently analyzed, as it is called, whether by a thick
block of Iceland spar furnished with screens so as to
stop out one of the transmitted pencils, or by any of the
more convenient methods more commonly employed.
Let the analyzer be turned till the field of view is
dark, the light falling upon the analyzer in that posi-
tion being stifled, as in the case of a good tourmaline,
or else sent elsewhere. If a block of Iceland spar
be interposed between the polarizer and the analyzer,
and turned round in its own plane, in general there is
more or less restoration of light, there being only
four azimuths of the block, separated by 90*, in a
RESTORATION OF LIGHT BY CRYSTAL, 10/
complete turn in which the field remains dark as
before the interposition of the block.
This restoration of light is very easily explained
as a consequence of what has already been mentioned.
The polarized light falling on the block is divided
into two beams polarized respectively in and perpen-
dicularly to its principal plane> which traverse the
crystal independently though overlapping, and which
emerge blended together. Each of these on entering
the analyzer is again divided into two, polarized in
rectangular planes, which are those of the plane of
primitive polarization and the perpendicular plane,
of which the latter alone is retained, and the two
retained portions of each of the streams enter the eye
together, and their illuminations are added together.
A very simple application of Malus's law shows that
if we take the intensity of the primitively polarized
light for unity, and disregard the small loss by
reflection, the intensity of the light entering the eye
will be half the square of the sine of double the
azimuth of the block, measured from one of the
vanishing positions. This restoration of light in
the dark field forms a very sensitive and easily
applied test of the possession of double refraction by
the substance interposed.
But an observation made by Arago about i8n
opened out quite a new field of research, remarkable
Id8 THE NATURE OF LIGHT.
alike for the beauty of the phenomena, for the light
they throw upon the nature of polarization, and for
the information they afford us respecting the inmost
structure of bodies. Arago found that when the in-
terposed crystalline plate was very thin, as may easily
be obtained with mica or sulphate of lime, the re-
stored light was not as before white, but showed the
most gorgeous colours, varying with the thickness of
the plate, its nature, and the direction in which and
amount by which it is inclined, if inclined it be.
The more powerfully doubly refracting be the
substance interposed, . the thinner as a rule is the
interposed plate required to be in order to show
these colours. But with a given substance, such for
example as Iceland spar, the amount of double
refraction varies immensely with the direction. Thus
in Iceland spar, one of the most powerfully doubly .
refracting substances known, we have seen that
in the direction of the axis the two rays are
refracted alike. Accordingly if a plate of Iceland
spar, even a thick plate, be cut perpendicular to the
axis, and be interposed perpendicularly to the inci-
dent light in the dark field, a splendid system of
coloured rings is seen, which are interrupted by a
dark cross. The arrangement of coloured curves is
still more remarkable in the case of biaxal crystals,
but the simpler case of a thin crystalline plate is
COLOURS OF CRYSTALLINE PLATES. IO9
better adapted to our present purpose, since in the
other case there are too many things crowded at
once upon the attention.
Let us revert then to the case of a thin crystalline
plate interposed in the dark field, being held, as
I will suppose, perpendicularly to the incident light.
Even with this restriction, it would take too long to
mention all the phenomena exhibited, and would be
wearisome; nor is it advisable to treat the subject
in this way, for in fact they have all been brought
under the dominion of theory, and are best studied
in connexion with it, except in so far as may be
necessary to establish the theory in the first instance.
I shall restrict myself therefore to mentioning a
few leading features of the phenomenon, premising
that in the case of a doubly refracting plate in
general, as in that of a block of Iceland spar, there
are two rectangular directions in which the beams
independently transmitted are respectively polarized,
and that if the incident light is polarized, and the
plane of polarization coincides with either of those
directions, the whole of the light entering the crystal
passes into the beam which is polarized in the plane
of primitive polarization. The two rectangular direc-
tions above mentioned have been named the neutral
axes of the plate.
If the thin crystalline plate interposed be of uni-
MO THE NATURE OF LIGHT.
form thickness, it is seen of a uniform colour ; if the
thickness vary irregularly, as in the case of a plate
of selenite obtained by casual cleavage, the colours
are arranged in patches, corresponding to the varying
thickness. If the plate be turned in its own plane,
there are four rectangular positions in which the
field is left dark as at first, which are those in which
one or other of the neutral axes lies in the plane
of primitive polarization, and in which accordingly
there is no bifurcation of the incident light on passing
into the crystal.
If the analyzer be turned through 90°, so that the
planes of polarization of the polarizer and analyzer
are now coincident instead of perpendicular, and the
field before the introduction of the crystal is at its
maximum of brightness, on interposing the crystal-
line plate the colours now seen are complementary
in character to the former. They vanish altogether
when either neutral axis comes into the plane of
primitive polarization, and are less vivid than in the
dark field except when the neutral axes are at an
azimuth of 45^ from the vanishing positions.
If the planes of polarization and analyzation be
set at an arbitrary angle, and the crystal be turned in
its own plane, there are eight positions in a com-
plete revolution in which the colours disappear, giving
place to white light of the same intensity as when the
COLOURS OF CRYSTALLINE PLATES. Ill
plate is away. Between these critical positions, the
colours have the character of those of the dark and
of the bright field alternately. The critical positions
are those in which one of the neutral axes lies in
the plane of polarization or analyzation. Hence —
and this is to be specially noticed — for the production
of the colours it is essential that the polarized light
we start with should be divided into two pencils
in passing through the crystal, and that each of these
again should be divided into two by the analyzer, of
which one portion is retained.
If the crystalline plate be ground into the form of
a slender wedge, the colours are arranged in bands
parallel to the edge of the wedge, the bands for any
colour being equidistant, and the scale larger for the
red than for the blue. If the analyzer be set to give
the dark and the bright field in succession, the tints
of the wedge agree with those of the reflected system
of Newton's rings in the former case, and the trans-
mitted system in the latter.
The equidistance of the bands for any particular
colour shows that the law of the order of the tints,
as depending on the thickness of the plate, is the
very same as in the case of Newton's rings, the
magnitude of the thickness merely being very much
greater than in that case. Nor is this all. If we
know the doubly refracting energy of any particular
112 THE NATURE OF LIGHT.
substance, suppose sulphate of lime, we can calculate
the retardation of phase of one relatively to the other
of the two rectangularly polarized pencils which a
thin plate of the substance can independently trans-
mit, in terms of the thickness of the plate, to which
that retardation is proportional. Now Dr Young
showed that when this is done the thickness of plate
by which any particular tint is produced is just what
it ought to be on the supposition that the colour is
due to the interference of the two rectangularly
polarized pencils which traversed the crystal inde-
pendently. After all this we can hardly help sup-
posing that the colours must in some way be due
to interference. But if so, why are they not seen
with common light, just as Newton's rings ; why
should it be necessary that the light should in some
way be polarized, and the polarized light should in
some way be analyzed, and that the crystalline plate
should be interposed between the polarizer and the
analyzer in order that any colours at all should be
seen ?
If we assume that the colours of crystalline plates
in polarized light are due to interference, the laws
of the interference of polarized light may be deduced
from the observation of those colours without any
experimental difficulty. But if it still be regarded as
in any way an open question whether those colours
INTERFERENCE OF POLARIZED LIGHT. II J
are due to interference, it becomes important to in-
vestigate those laws by means of experiments free
from any such doubt.
Accordingly the series of researches by which
Arago and Fresnel determined in a direct manner*
the laws of interference of polarized light must be
regarded as making an epoch in the progress of the
study of this branch of the subject. These experi-
ments were made on the fringes of interference with
which we had already become familiar as exhibited
by common light; such fringes as those produced
by the interference of two streams of light from the
same source, such as two virtual images of a lumin-
ous point, or of two streams from the same luminous
point, which after passing through two parallel ex-
tremely narrow apertures near one another diverged
and mixed together. We have seen what a trium-
phant explanation the theory of undulations affords
of the phenomena of interference and diffraction in
the case of common light ; and if we obtain the same
fringes, with the appearance of which we are so
familiar, in working with polarized instead of com-
mon light, we cannot refuse to admit that they too
are due to interference.
The study of the interference of two streams of
light polarized in the same way presents no experi-
mental difficulty whatsoever. It is merely necessary
S. 8
114 THE NATURE OF LIGHT.
to use polarized light instead of common light in
any of the ordinary experiments of .interference. On
doing this the phenomena of interference are found
to be absolutely the same with polarized as with
common light. But to polarize two portions of light
from the same source, and proceeding nearly along
the same course, in two rectangular directions, and
yet ensure a very near equality in the lengths of their
paths, or rather equivalent paths in air, is a matter
of very great nicety, so small is the difference of
path that would suffice to prevent any exhibition
of interference of the usual kind. Nevertheless by
a series of ingeniously devised and carefully executed
experiments Arago and Fresnel succeeded in estab-
lishing conclusively under what circumstances polar-
ized light is, and under what it is not, capable of
manifesting the usual phenomena of interference.
The result of this enquiry was summed up in five
laws relating to the interference of polarized light,
which were derived directly from observation. One
of these has already been mentioned. Another is
that when two streams of light from the same source
are polarized in rectangular planes, they show no
phenomena of interference, notwithstanding a near
equality of paths. Another, that the mixed stream
as in the last case may be analyzed without any
phenomena of interference being thereby revealed.
INTERFERENCE OF POLARIZED LIGHT. 1 15
Another that when two streams of light from the
same source are polarized in rectangular planes, and
afterwards analyzed, they do manifest the phenomena
of interference provided the original source were one
of polarized instead of common light. Lastly, in the
phenomena of interference produced by rays which
have experienced double refraction, the place of the
fringes is not in all cases determined solely by the
difference of equivalent paths ; in certain cases it is
necessary to alter the difference of paths by half
an undulation. And the rule they gave for deter-
mining under what circumstances the half undulation
should be added and under what circumstances not
amounted to this :— when the planes of polarization
and analyzation lie in the same quadrant made by
the neutral axes of the crystalline plane, the cha-
racter of the interference is determined simply by
the difference of paths ; but when they lie in adjacent
quadrants, we must alter the difference of paths by
half an undulation.
These five empirical laws embrace the necessity
for a polarizer and for an analyzer in order that colours
should be seen in a crystalline plate; and taken in
conjunction with Malus's law, regarded at present
merely as an empirical law, they enable us to cal-
culate completely the colours of crystalline plates
under all the varied conditions which may exist as
8—2
Il6 THE NATURE OK LIGHT.
to thickness of the plate, doubly refracting energy
of the substance of which it is formed, azimuth of
the neutral axes relatively to the plane of primitive
polarization, azimuth of the plane of analyzation ;
and for that we have no occasion to enter into any
speculation at all as to what it is that constitutes
polarization. Nay more; if we take the laws of
double refraction as known empirically as the result
of direct observation, we may even calculate com-
pletely the coloured rings and curves about the optic
axis or axes of uniaxal or biaxal crystals, without
entering into any speculation as to what the theo-
retical interpretation of polarization may be.
The question now arises, can we embrace the five
laws of interference of polarized light, and Malus's
law, in a theory which shall comprehend them all,
and which shall be at least hopeful for the explanation
of double refraction and of the polarization of Vi^ht by
reflection ; though as these may depend on a know-
ledge of what is the actual state of things which we
do not possess, we cannot demand of necessity that
it sAa/l lead to their explanation.
In applying Malus's law to the calculation of the
colours of crystalline plates, we are led to contem-
plate an intensity which we may take as unity in the
incident original polarized light as giving rise to
intensities cos* A and sin* A belonging to light
TRANSVERSE VIBRATIONS. 11/
polarized in a plane making an angle A with the
plane of primitive polarization and in the perpen-
dicular plane respectively, and these again as giving
rise to polarized beams the intensities of which are
obtained by a re-application of the very same law.
Now in studying the interference of common light,
we saw reason to conclude that for light of a given
kind, that is, of a given refrangibility, the intensity is
measured by the square of the coefficient of vibra-
tion, and consequently the coefficient of vibration
by the square root of the intensity. It is true that
I have not been able to lay before you the full
evidence on which this conclusion is based, as it
would have involved some considerations of too
mathematical a nature to be suitable to the present
lectures, so that I have been obliged to leave the
result to be accepted in some measure on the strength
of authority. Consequently we are led by pure
observation, combined with so much of theory as
belongs to the study of common light, to contem-
plate a beam of polarized light in which the co-
efficient of vibration may be taken as unity as being
divided (as for example in passing through a crystal-
line lamina) into two polarized in rectangular planes,
at azimuths of A and 90^— A to the plane of primitive
polarization, the coefficients of vibration belonging to
which are expressed by cos^ and sin^. But this is
Il8 THE NATURE OF LIGHT,
identically the law according to which forces, or dis-
placements, or velocities in directions perpendicular to
that of propagation, and in or equally inclined to the
planes of polarization, would be resolved. We are
inevitably driven to the contemplation of a something
about polarized light which admits of composition
and resolution according to the above simple law.
This "something*- can hardly be other than the
vibrations themselves, and we are thus led to conclude
that in polarized light the vibrations are rectilinear,
but instead of being in the direction of propagation,
as from the analogy of sound the vibrations of Light
might naturally have been expected to be, are trans-
verse to the direction of propagation.
When polarized light is obtained by ordinary
refraction through Iceland spar, or by reflection from
glass at the proper angle or incidence, everything is
symmetrical with respect to the plane of polarization.
We must suppose therefore that in polarized light
the vibrations are symmetrical with respect to the plane
of polarization. This leaves two alternatives open :
they may either be in the plane of polarization or
perpendicular to the plane of polarization. So far as
the explanation of the laws of interference of polarized
light is concerned, it is a matter of absolute in-
difference which alternative we adopt, and some
undulationists have adopted the one and some the
TRANSVERSE VIBRATIONS. II 9
other. The question can only be decided, if it can be
decided at all, by introducing more or less of dy-
namical considerations, and that introduces more or
less of speculation, since the dynamical nature of the
mutual action of ponderable matter and ether is in
great measure unknown to us. Perhaps the argument
which introduces least speculation as to the dy-
namical nature of such actions is that derived from
diffraction at a considerable angle ; though it is true
that even here we cannot produce that diffraction
without the intervention of ponderable matter. The
result in this case, as I have elsewhere shown, is
decidedly in favour of the supposition that the vibra-
tions are perpendicular to the plane of polarization,
which is the alternative that was adopted by Fresnel,
and ultimately by Cauchy, though at first he adopted
the other ; and it is the one for which, independently
of diffraction, there is I think the most to be said.
But as I have remarked the theory of transverse
vibrations taken by itself does not involve the decision
of this question.
If such be the nature of polarized light, what
notion are we to form as to the nature of common
light ? Suppose light coming in some definite direc-
tion to fall on a screen with a hole, and to be
received at the other side on a block of Iceland spar.
Then if the hole be not too large, the two beams
I20 THE NATURE OF LIGHT.
which are produced within the spar will come out
separated from one another, and will show their
polarization in rectangular planes. This will still be
true however the screen may be moved about, so that
the light falls on different parts of the face of the
block. Now let the screen be removed altogether.
The light will still be decomposed into two beams
within the spar, giving rise on emergence to two
beams polarized in rectangular planes, but the beams
will be broad, and will mix on emergence. But the
mixture is identical with, or at any rate is undis-
tinguishable from, common light* Now the two
disturbances in rectangular planes give rise by their
composition to a disturbance which is in the fronts of
the waves, but is in general elliptical, including the
extreme cases of circular and rectilinear vibrations,
but with the elements of the ellipse changing, as we
have every reason to expect, irregularly in all sorts of
ways a great number of times in a second. For
though the vibrations may be sensibly regular for
thousands or it may be myriads together (and the
phenomena of interference show that they must have
* Abstraction is here made of the loss by reflectioxi, which is not
quite the same for the ordinary and extraordinary, the higher refraction
of the former being accompanied by a slightly more copious reflection,
so that in the transmitted light there is a slight theoretical preponder-
ance of intensity in favoor of the extraordinary. This is however so
small as to be barely sensible in refined experiments, and for onr present
purpose it is best neglected.
TRANSVERSE VIBRATIONS. 121
a high degree or regularity) yet we should have no
reason a priori to expect that they would remain
regular for the fifty millions of millions or so of vibra-
tions which must take place in the tenth of a second,
the time for which an impression made on the retina
is estimated to last.
Such being our notion of common light, the division
of common light into two rectangularly polarized beams
which follow different paths must be taken to imply
that for some cause yet to be investigated the vibra-
tions, which at first were in the fronts of the waves,
but in other respects of any kind, are decomposed
into two rectilinear vibrations in rectangular directions,
which are propagated along different paths.
This fundamental conception as to the nature of
polarized light, and its relation to common light, ex-
plains in the simplest manner the six laws relating to
the interference of polarized light, and to the intensity
of the polarized streams into which polarized light may
be divided, to which I have just referred. The inter-
ference of light merely demands, so far as direction
of vibration is concerned, that it should be as nearly
as possible the same for the two interfering streams,
a condition satisfied by two streams polarized in the
same way. Again, the kinetic energy of a set of
vibrations, to which for light of a given kind the
intensity is theoretically proportional, is the sum of
122 THE NATURE OF LIGHT.
the kinetic energies of the components in any two
rectangular directions, irrespective of their difference
of phase, and therefore no phenomena of interference
ought to be visible in the mixture of two rectangularly-
polarized portions of light, even though they came
originally from the same polarized source. Again, if
common light be divided into two rectangularly-
polarized portions, which are afterwards subdivided
in a similar manner, and a pair of these latter com-
ponents which are polarized alike mix, having had
but a small difference of path from the original source,
they ought not to show any signs of interference.
For as there is no fixed and permanent relation
between the relative magnitudes or the relative
starting-times of the first components, they are as
good as if they came from two independent sources,
in which case no phenomena of interference are
either theoretically observable or experimentally ob-
served, do what we will with the streams of light
afterwards. But if the original source of light be one
of polarized instead of common light, the case is
altogether different. Then, whatever changes take
place during the tenth of a second in the amplitude
or starting-time of one of the first components, exactly
the same take place in the other, and are carried on
into the second components, of which therefore those
which are polarized in the same way are in a condition
ELLIPTICALLY POLARIZED LIGHT. 1 23
to interfere. And ats to the circumstances under
which in this kind of interference the difference of
path must sometimes be imagined altered by half an
undulation, the matter is simple to the last degree on
the theory of transverse vibrations ; it merely involves
attention to the sign of a geometrical projection ; and
if we express the intensity of the mixed light, for the
case in which the planes of polarization and analyza-
tion lie in the same quadrant formed by the neutral
axes of a crystalline plate, by a formula in which the
symbols denote displacements or velocities or of an
ethereal particle instead of intensities, the formula
takes care of itself, and applies equally to the case in
which the planes of polarization and analyzation lie
in adjacent quadrants.
If polarized light be incident on a crystalline plate
of uniform thickness, and the emergent light be
viewed through an analyzer which is turned round,
then except in certain special cases which I need not
particularize, the light is not extinguished by the
analyzer however it be turned, but merely be-
comes, in general, alternately a maximum and a
minimum alternately at every quarter of a turn. So
far it agrees exactly with partially polarized light.
And yet the two are altogether different, and the
difference may be seen at a glance by viewing them
through a Nicol's prism capped by a plate of Iceland
124 THE NATURE OF LIGHT.
spar cut perpendicular to the axis. The h'ght we are
now considering is called elliptically polarized light,
and in contradistinction to it the light which I have
hitherto called polarized has been denominated plane-
polarized.
Elliptically polarized light may be obtained inde-
pendently altogether of double refraction. The theory
of transverse vibrations presents to the mind a very
clear picture of what constitutes it. But as this
is a matter of detail not involving any fresh principle,
I forbear to enter further into it.
Being now armed with a definite theory as to the
nature of polarized light, we are prepared to consider
whether any explanation can be given of double
refraction, as an accompaniment of which polarization
was first discovered. Whether we are able or not to
give a complete explanation of it, we might expect
that the theory would at least so far fall in with it as
to point hopefully towards an explanation.
The most salient feature of double refraction,
interpreted by the aid of the theory which makes
light to consist in undulations, and of that which
specifies the nature of polarized light, is that when
light falls on a crystalline plate or prism it gives rise
to two kinds of disturbance within the crystal, which
are propagated with different velocities, and in which
the vibrations are rectilinear, and take place in planes
EXPLANATION OF DOUBLE REFRACTION. 125
which are perpendicular to each other, or at least
very approximately so, and of- which the directions
are determined by lines fixed in the crystal.
Now we have not far to go to find a mechanical
illustration of such a mode of action. Imagine an
elastic rod terminated at one end, and extending
indefinitely in the other direction. Let the rod be
rectangular in section, the sides of the rectangle
being unequal, so that the rod is stifier to resist
flexure in one of its principal planes than the other.
Let this rod be joined on to a cylindrical rod forming
a continuation of it which extends indefinitely. Con-
ceive the compound rod as capable of propagating
small transverse disturbances in which the axis of the
rod suffers flexure. Imagine a small disturbance,
3uppose periodic, to be travelling in the cylindrical
rod towards the junction. It will travel on without
change of type even though the flexure of the axis be
not in one plane. But to find what disturbance it
excites in the rectangular rod, we must resolve the
disturbance in the cylindrical rod into its components
in the principal planes of the rectangular rod, and con-
sider them separately. Each will give rise in the rec-
tangular rod to a disturbance in its own plane, but the
two will travel along the rod with different velocities.
This illustrates the subdivision of a beam of common
light falling on a block of Iceland spar into two beams
I20 THE NATURE OF LIGHT.
polarized in rectangular planes, which are propagated
in the spar with different velocities. Again, suppose
the original disturbance in the cylindrical rod confined
to one plane. If this be either of the principal planes
of the rectangular rod, the more slowly or the more
quickly travelling kind of disturbance, as the case
may be, will alone be excited in the latter ; and if the
plane of the original disturbance be any other, the
components into which we must resolve it in order to
find the disturbance excited in the rectangular rod
will in general be of unequal intensity, their squares
varying with the azimuth of the plane of the original
disturbance in accordance with Malus's law. This
illustrates the subdivision of a beam of polarized light
incident on Iceland spar into two of unequal intensity
polarized in rectangular planes, and their alternate
disappearance at every quarter of a turn. We see
with what perfect simplicity the theory of transverse
vibrations falls in with the elementary facts of polari-
zation discovered by Huygens, standing in marked
contrast in this respect with the conjecture by which
Huygens himself attempted to account for double
refraction.
But can we go further, and account for, or
discover, from theory the laws of double refraction
and the accompanying polarization in different direc-
tions in doubly refracting crystals ?
FRESNEL*S LAW OF DOUBLE REFRACTION. 12/
It is to Fresnel we owe the first theoretical deduc-
tion of the laws of double refraction in Iceland spar,
and the discovery of the beautiful laws of double refrac-
tion in biaxal crystals ; laws some of which had been
previously known from observation, while in other
respects theory served to correct what had been
supposed to be the result of observation, but which
more careful observation carried out in directions indi-
cated by theory proved to have been incorrect. The
generalization by which Fresnel passed from the laws
of double refraction in uniaxal to those in biaxal
crystals is one of the most splendid things which has
been done in science. And yet the theory which
guided him to the discovery of these laws is not one
which is rigorous throughout, nor did Fresnel himself
profess that it was, though in some reproductions of
his theory contained in text-books it is presented as
if it were, to the detriment of the student. Fresnel
was a man of singular sagacity, endowed apparently
with a mind of the inductive class, leading him often
to the discovery of truth from conflicting or imperfect
evidence. We may even say it is fortunate that
Fresnel did not rigorously follow out to their con-
clusions the premises with which he started, for had he
done so he would have missed the discovery of the
elegant laws of double refraction. In fact, Cauchy
and Neumann independently worked out the con-
128 THE NATURE OF LIGHT.
elusions which rigorously follow from the state of
things assumed by Fresnel ; but with all the squeezing
which the arbitrary constants furnished by theory
admit of, they were not able to obtain Fresnel's laws
except as an approximation. Had this been all, it is
possible that the more complicated laws expressed by
their formulae might have fitted observation as well as
the simpler and more elegant laws of Fresnel. But
the theory is hampered by a third ray which cannot
be got rid of, and which leads to conclusions at
variance with observation. While admiring therefore
the geometrical part of Fresnel's theory, we must
reject the mechanical conditions which he supposed to
exist in crystals, as not being in conformity with
nature.
Fresnel's laws have been obtained in an extremely
elegant manner, as the result of a rigorous theory, by
Green, who starting with an assumed mechanical state
inclusive of but more general than that assumed by
Fresnel, and subsequently limiting the generality by
a single condition which the phenomena of light
would naturally lead us to introduce, arrived directly
at Fresnel's laws. It was necessary however to sup-
pose the vibrations of polarized light to be in the
plane of polarization. In the same paper he showed
however that by starting with a mechanical state still
more general, limiting it as before, and introducing
THEORIES OF DOUBLE REFRACTION. 1 29
two simple linear relations between the arbitrary
constants remaining, Fresnel's laws were again ob-
tained, but this time by supposing that in polarized
light the vibrations are perpendicular to the plane of
polarization. Almost simultaneously with Green
MacCullagh obtained equations of motion of the
ether in a crystal identical with those of Green in his
first theory, though by a method which does not seem
quite so satisfactory as that of Green. They led of
course to the same laws, and required the same
supposition as to the direction of the vibrations in
polarized light. Lam6 has given a theory sub-
stantially agreeing with Green's first theory ; and last
but not least we have the electro-magnetic theory of
Maxwell, which without any straining or assumption
of relations between constants leads directly to
FresneFs laws.
It may seem strange that we should arrive at the
very same laws by such difTerent theories; first by
one which is not a rigorous theory at all, and then by
others which are rigorous, but which differ among
themselves, even to such an extent that in one the '
vibrations in polarized light must be assumed to be
in, in another perpendicular to the plane of polariza-
tion. In explanation of this it is to be observed, first,
that all these theories alike involve the idea of
transverse vibrations, and secondly that Fresnel's laws
S. 9
n
130 THE NATURE OF LIGHT.
are really the simplest which can in any way suit the
phenomena. Fresnel's laws are embraced in an
elegant construction applied to an ellipsoid ; and just
as an ellipsoid is the simplest generalization of a
sphere when we pass from what is alike in all directions
to what varies from one direction to another, so
Fresnel's laws are really the simplest that the nature
of the phenomenon, viewed in the light of the
theory of transverse vibrations, admits of. It is not
therefore so wonderful as at first sight might appear
that the same laws should be arrived at from theories
so different ; and while the deduction of these laws is .
a strong confirmation of the truth of the theory of
transverse vibrations which is common to all the
methods, it is not itself alone to be taken as establish-
ing the truth of the supposition as to the mechanical
state of things in crystals which has been made in the
deduction of the laws.
I have mentioned Malus's discovery of the polari-
zation of light by reflection, and the question may
naturally arise, is this reconcileable with the theory of
transverse vibrations.? To show that it is, I need
only refer to Fresnel's deduction of the intensity of
the light reflected from an isotropic transparent
medium, according as the vibrations are in or per-
pendicular to the plane of incidence. These formulae
were obtained by Fresnel with his wonted sagacity
THEORIES OF OTHER PHENOMENA. 131
from a process only partially complete, since we must
either allow that a part only of the necessary equations
of condition at the common boundary of the media
are satisfied, or else that the mechanical state for
which the conditions employed give the complete
solution remains to be defined.
FresneFs deduction of his laws for the intensity of
reflected light was made on the supposition that in
polarized light the vibrations are perpendicular to the
plane of polarization. A slight difference of hypo-
thesis as to the state of things would lead, by reason-
ing very similar to that of Fresnel, to the very same
two formulae only with the directions of vibration to
which they respectively apply interchanged. On the
present supposition therefore the vibrations in polarized
light must be supposed to be in the plane of polari-
zation.
The polarization of light through the unequal
absorption belonging to the two rectangularly polarized
pencils within certain coloured doubly refracting
crystals, such as tourmaline, readily falls in with the
theory of transverse vibrations. For there can be no
doubt that absorption in general consists in the ex-
penditure of the incident ethereal vibrations in pro-
ducing molecular agitation; and it is easily under-
stood that the molecules may be more easily agitated
by an ethereal vibration in one direction than in
another.
IJ!^ THE NATURE OF LIGHT.
The aim which I have proposed to myself in this
first course of the Burnett lectures has been to lay
before you, as impartially as I could, a summary of
the evidence on which we accept the answer to the
question. What is Light ? given when we say. Light
consists of undulations in a medium, called ether, per-
vading the interplanetary and interstellar spaces, and
existing also within bodies formed of ponderable
matter. Difference of refrangibility, with the ac-
companying difference of colour, depends upon a
difference in the frequency of these undulations. The
direction of vibration of the particles of the ether is
transverse to the direction of propagation of the
light, and accordingly (at any rate in the case of
vacuum or an isotropic medium) the vibrations take
place in the fronts of the waves, but in common light
are not otherwise restricted, while in polarized light
they are rectilinear, taking place in a direction which
is symmetrical with respect to the plane of polari-
zation.
Naturally the full force of the evidence can be felt
only by those who have well studied the subject, I
hope however that I may have succeeded in showing,
even to those who previously may have paid little
attention to the matter, that at least there are powerful
arguments in favour of the accepted answer. The
inductive arrangement, which seemed best fitted for
CONCLUSION OF FIRST COURSE. 1 33
the object I had in view, naturally led to a treatment
in good measure historical, but I have not, I hope,
neglected recent researches. I have endeavoured to
discriminate, and to lead you to discriminate, between
what is well established and what is still speculative,
and have confined myself almost entirely to the
former.
Should I be permitted to deliver courses of
lectures again in the two following years, it is my
intention, in accordance with a scheme communicated
in outline to and approved by the Burnett Trustees, to
devote next year's course to researches in which
light has been used as a means of investigation,
while the third year's course would be assigned to
light considered in relation to its beneficial effects.
While the different objects to be held in view in
these lectures are more or less blended together, the
second course would more especially relate to recent
researches, while the third would naturally harmonize
with the original intentions of the Founder of the
Trust.
END OF FIRST COURSK
CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. & SON, AT THE UNIVERSITY PRESS.
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